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Pertanyaan

Jika diketahui begin mathsize 14px style left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis equals straight x to the power of 4 minus 10 straight x squared plus 19 end style dan begin mathsize 14px style straight g left parenthesis straight x right parenthesis equals straight x squared minus 3 end style. Maka fungsi begin mathsize 14px style straight f left parenthesis straight x right parenthesis end style adalah ....

  1. begin mathsize 14px style straight x squared minus 4 straight x minus 2 end style 

  2. Error converting from MathML to accessible text. 

  3. Error converting from MathML to accessible text. 

  4. Error converting from MathML to accessible text. 

  5. Error converting from MathML to accessible text. 

Pembahasan Soal:

Diketahui:

begin mathsize 14px style left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis equals straight x to the power of 4 minus 10 straight x squared plus 19 end style dan begin mathsize 14px style straight g left parenthesis straight x right parenthesis equals straight x squared minus 3 end style.

Ditanya:

Tentukan fungsi begin mathsize 14px style straight f left parenthesis straight x right parenthesis end style.

Solusi:

Dengan konsep komposisi fungsi, diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight f left parenthesis straight g left parenthesis straight x right parenthesis right parenthesis end cell equals cell left parenthesis straight f ring operator straight g right parenthesis left parenthesis straight x right parenthesis end cell row cell straight f left parenthesis straight x squared minus 3 right parenthesis end cell equals cell straight x to the power of 4 minus 10 straight x squared end cell end table end style 

Misalkan begin mathsize 14px style straight y equals straight x squared minus 3 rightwards arrow straight x squared equals straight y plus 3 end style, Sehingga diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight f left parenthesis straight x squared minus 3 right parenthesis end cell equals cell straight x to the power of 4 minus 10 straight x squared plus 19 end cell row cell straight f left parenthesis straight x squared minus 3 right parenthesis end cell equals cell left parenthesis straight x squared right parenthesis squared minus 10 straight x squared plus 19 end cell row cell straight f left parenthesis straight y right parenthesis end cell equals cell left parenthesis straight y plus 3 right parenthesis squared minus 10 left parenthesis straight y plus 3 right parenthesis plus 19 end cell row blank equals cell straight y squared plus 6 straight y plus 9 minus 10 straight y minus 30 plus 19 end cell row blank equals cell straight y squared minus 4 straight y minus 2 end cell row cell straight f left parenthesis straight x right parenthesis end cell equals cell straight x squared minus 4 straight x minus 2 end cell end table end style  

Jadi, Fungsi begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight f left parenthesis straight x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell x squared end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 4 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 2 end table end style.

Oleh karena itu, Jawaban yang benar adalah A

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

R. RGFLLIMA

Terakhir diupdate 30 April 2021

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Pertanyaan yang serupa

Jika diketahui  dan , rumus fungsi  adalah ....

Pembahasan Soal:

Dengan menerapkan rumus komposisi dua fungsi, diperoleh perhitungan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell 4 x squared minus 10 x plus 21 end cell row cell f open parentheses g open parentheses x close parentheses close parentheses end cell equals cell 4 x squared minus 10 x plus 21 end cell row cell f open parentheses 2 x plus 3 close parentheses end cell equals cell 4 x squared minus 10 x plus 21 end cell end table end style 

Misalkan begin mathsize 14px style 2 x plus 3 equals u end style sehingga begin mathsize 14px style x equals fraction numerator u minus 3 over denominator 2 end fraction end style. Selanjutnya diperoleh perhitungan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses 2 x plus 3 close parentheses end cell equals cell 4 x squared minus 10 x plus 21 end cell row cell f open parentheses u close parentheses end cell equals cell 4 space open parentheses fraction numerator u minus 3 over denominator 2 end fraction close parentheses squared minus up diagonal strike 10 to the power of space 5 space end exponent open parentheses fraction numerator u minus 3 over denominator up diagonal strike 2 end fraction close parentheses plus 21 end cell row blank equals cell up diagonal strike 4 space open parentheses fraction numerator u squared minus 6 u plus 9 over denominator up diagonal strike 4 end fraction close parentheses minus open parentheses 5 u minus 15 close parentheses plus 21 end cell row blank equals cell u squared minus 6 u plus 9 minus 5 u plus 15 plus 21 end cell row blank equals cell u squared minus 11 u plus 45 end cell row cell f open parentheses x close parentheses end cell equals cell x squared minus 11 x plus 45 end cell end table end style 

Jadi, rumus fungsi begin mathsize 14px style f open parentheses x close parentheses end style adalah begin mathsize 14px style x squared minus 11 x plus 45 end style.

Dengan demikian, jawaban yang tepat adalah C.

Roboguru

Diketahui fungsi  dan  dengan  dan , maka nilai  adalah ....

Pembahasan Soal:

Diketahui:

table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis x right parenthesis end cell equals cell negative x plus 3 end cell row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell 4 x squared minus 26 x plus 32 end cell end table 

Perhatikan bahwa f open parentheses 1 close parentheses diperoleh ketika g open parentheses x close parentheses equals 1. Sehingga dapat ditentukan x agar g open parentheses x close parentheses equals 1 sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell g open parentheses x close parentheses end cell equals 1 row cell negative x plus 3 end cell equals 1 row x equals cell 3 minus 1 end cell row x equals 2 end table 

Sehingga dapat ditentukan nilai f open parentheses 1 close parentheses sebagai berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses 1 close parentheses end cell equals cell f open parentheses g open parentheses x close parentheses equals 1 close parentheses end cell row blank equals cell f open parentheses g open parentheses 2 close parentheses close parentheses end cell row blank equals cell 4 times 2 squared minus 26 times 2 plus 32 end cell row blank equals cell 16 minus 52 plus 32 end cell row blank equals cell negative 4 end cell end table 

Jadi, jawaban yang benar adalah B.

Roboguru

Diketahui dan , maka tentukan

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell 12 x minus 8 end cell row cell f open parentheses g open parentheses x close parentheses close parentheses end cell equals cell 12 x minus 8 end cell row cell f open parentheses 4 x minus 3 close parentheses end cell equals cell 12 x minus 8 end cell end table end style

Kita misalkan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell 4 x minus 3 end cell row cell 4 x end cell equals cell negative y minus 3 end cell row x equals cell fraction numerator negative y minus 3 over denominator 4 end fraction end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis 4 x minus 3 right parenthesis end cell equals cell 12 x minus 8 end cell row cell f left parenthesis y right parenthesis end cell equals cell 12 left parenthesis fraction numerator negative y minus 3 over denominator 4 end fraction right parenthesis minus 8 end cell row cell f left parenthesis y right parenthesis end cell equals cell negative 3 y minus 9 minus 8 end cell row cell f left parenthesis y right parenthesis end cell equals cell negative 3 y minus 17 end cell row cell f left parenthesis x right parenthesis end cell equals cell negative 3 x minus 17 end cell row blank blank blank end table end style

Jadi, begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell f left parenthesis x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 3 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 17 end table end style  

 

Roboguru

Tentukan  jika: a.  dan

Pembahasan Soal:

begin mathsize 14px style left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end style artinya g dimasukkan ke f

begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses equals f open parentheses g open parentheses x close parentheses close parentheses end style 

Misal begin mathsize 14px style x squared plus 3 x minus 2 equals a end style diperoleh 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x squared plus 3 x minus 2 end cell equals a row cell x squared plus 3 x end cell equals cell a plus 2 end cell row blank blank blank end table end style

begin mathsize 14px style 2 x squared plus 6 x plus 1 equals 2 left parenthesis x squared plus 3 x right parenthesis plus 1 2 x squared plus 6 x plus 1 equals 2 left parenthesis a plus 2 right parenthesis plus 1 end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell f open parentheses g open parentheses x close parentheses close parentheses end cell row cell 2 x squared plus 6 x plus 1 end cell equals cell f open parentheses x squared plus 3 x minus 2 close parentheses end cell row cell 2 left parenthesis a plus 2 right parenthesis plus 1 end cell equals cell f open parentheses a close parentheses end cell row cell 2 a plus 4 plus 1 end cell equals cell f open parentheses a close parentheses end cell row cell 2 a plus 5 end cell equals cell f open parentheses a close parentheses end cell row blank blank blank row blank blank blank end table end style 

begin mathsize 14px style f open parentheses x close parentheses equals 2 x plus 5 end style  

Jadi, nilai dari begin mathsize 14px style f left parenthesis x right parenthesis end style adalah begin mathsize 14px style 2 x plus 5 end style  undefined 

Roboguru

Jika  dan , nilai ....

Pembahasan Soal:

begin mathsize 14px style left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis equals left parenthesis log open parentheses x close parentheses right parenthesis squared plus 2 log open parentheses x close parentheses plus 1 g open parentheses f open parentheses x close parentheses close parentheses equals left parenthesis log open parentheses x close parentheses right parenthesis squared plus 2 log open parentheses x close parentheses plus 1 end style

Masukan begin mathsize 14px style f left parenthesis x right parenthesis end style ke begin mathsize 14px style g left parenthesis x right parenthesis equals left parenthesis x plus 1 right parenthesis squared end style, sehingga:

begin mathsize 14px style open parentheses f left parenthesis x right parenthesis plus 1 close parentheses squared equals left parenthesis log open parentheses x close parentheses right parenthesis squared plus 2 log open parentheses x close parentheses plus 1 end style

Ingat : begin mathsize 14px style left parenthesis a plus b right parenthesis squared equals a squared plus 2 a b plus b squared end style

size 14px left parenthesis size 14px f begin mathsize 14px style left parenthesis x right parenthesis end style size 14px plus size 14px 1 size 14px right parenthesis to the power of size 14px 2 size 14px equals begin mathsize 14px style left parenthesis l o g open parentheses x close parentheses plus 1 right parenthesis end style to the power of size 14px 2 begin mathsize 14px style left parenthesis left parenthesis f open parentheses x close parentheses plus 1 right parenthesis squared right parenthesis end style to the power of size 14px 1 over size 14px 2 end exponent size 14px equals begin mathsize 14px style left parenthesis left parenthesis log open parentheses x close parentheses plus 1 right parenthesis squared right parenthesis end style to the power of size 14px 1 over size 14px 2 end exponent size 14px f begin mathsize 14px style left parenthesis x right parenthesis end style size 14px plus size 14px 1 size 14px equals size 14px log begin mathsize 14px style left parenthesis x right parenthesis end style size 14px plus size 14px 1 size 14px f begin mathsize 14px style left parenthesis x right parenthesis end style size 14px plus size 14px 1 size 14px minus size 14px 1 size 14px equals size 14px log begin mathsize 14px style left parenthesis x right parenthesis end style size 14px plus size 14px 1 size 14px minus size 14px 1 size 14px f begin mathsize 14px style left parenthesis x right parenthesis end style size 14px equals size 14px log begin mathsize 14px style left parenthesis x right parenthesis end style size 14px left parenthesis size 14px f begin mathsize 14px style left parenthesis x right parenthesis end style size 14px plus size 14px 1 size 14px right parenthesis to the power of size 14px 2 size 14px equals begin mathsize 14px style left parenthesis l o g open parentheses x close parentheses plus 1 right parenthesis end style to the power of size 14px 2 begin mathsize 14px style left parenthesis left parenthesis f open parentheses x close parentheses plus 1 right parenthesis squared right parenthesis end style to the power of size 14px 1 over size 14px 2 end exponent size 14px equals begin mathsize 14px style left parenthesis left parenthesis log open parentheses x close parentheses plus 1 right parenthesis squared right parenthesis end style to the power of size 14px 1 over size 14px 2 end exponent size 14px f begin mathsize 14px style left parenthesis x right parenthesis end style size 14px plus size 14px 1 size 14px equals size 14px log begin mathsize 14px style left parenthesis x right parenthesis end style size 14px plus size 14px 1 size 14px f begin mathsize 14px style left parenthesis x right parenthesis end style size 14px plus size 14px 1 size 14px minus size 14px 1 size 14px equals size 14px log begin mathsize 14px style left parenthesis x right parenthesis end style size 14px plus size 14px 1 size 14px minus size 14px 1 size 14px f begin mathsize 14px style left parenthesis x right parenthesis end style size 14px equals size 14px log begin mathsize 14px style left parenthesis x right parenthesis equals to the power of 10 log left parenthesis x right parenthesis end style  

 

begin mathsize 14px style f left parenthesis 0 comma 0001 right parenthesis equals to the power of 10 log space left parenthesis 0 comma 0001 right parenthesis f left parenthesis 0 comma 0001 right parenthesis equals to the power of 10 to the power of 1 end exponent log space 10 to the power of negative 4 end exponent f left parenthesis 0 comma 0001 right parenthesis equals negative 4 end style(Sifat Logaritma begin mathsize 14px style blank to the power of a to the power of n end exponent log space a to the power of m equals m over n end style)

 

Jadi, jawaban yang tepat adalah D.

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