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Diketahui f(x)=2x−5 dan g(x)=3x2+1. Jika (f∘g)(x)=3, nilai x yang memenuhi adalah ...

Pertanyaan

Diketahui begin mathsize 14px style f open parentheses x close parentheses equals 2 x minus 5 end style dan begin mathsize 14px style g open parentheses x close parentheses equals 3 x squared plus 1 end style. Jika begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses equals 3 end style, nilai begin mathsize 14px style x end style yang memenuhi adalah ...

Pembahasan Soal:

Diketahui: begin mathsize 14px style f open parentheses x close parentheses equals 2 x minus 5 end style dan begin mathsize 14px style g open parentheses x close parentheses equals 3 x squared plus 1 end style.  Jika begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses equals 3 end style maka dengan menggunakan definisi fungsi komposisi diperoleh:

  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 3 row cell f open parentheses g open parentheses x close parentheses close parentheses end cell equals 3 row cell f open parentheses 3 x squared plus 1 close parentheses end cell equals 3 row cell 2 open parentheses 3 x squared plus 1 close parentheses minus 5 end cell equals 3 row cell 6 x squared plus 2 minus 5 end cell equals 3 row cell 6 x squared minus 3 end cell equals 3 row cell 6 x squared end cell equals cell 3 plus 3 end cell row cell 6 x squared end cell equals 6 row cell x squared end cell equals 1 row x equals cell plus-or-minus square root of 1 end cell row x equals cell plus-or-minus 1 end cell end table end style

Dengan demikian, diperoleh nilai begin mathsize 14px style x end style yang memenuhi adalah begin mathsize 14px style x equals 1 end style atau begin mathsize 14px style x equals negative 1 end style

Oleh karena itu, jawaban yang bener adalah B.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

S. Amamah

Mahasiswa/Alumni Universitas Negeri Malang

Terakhir diupdate 06 Oktober 2021

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Pertanyaan yang serupa

Diketahui f(x)=x2−4x+2dang(x)=3x+5. Fungsi komposisi (f∘g)(x)=....

Pembahasan Soal:

left parenthesis f o g right parenthesis left parenthesis x right parenthesis equals f left parenthesis g left parenthesis x right parenthesis right parenthesis  f left parenthesis 3 x plus 5 right parenthesis equals left parenthesis 3 x plus 5 right parenthesis squared minus 4 left parenthesis 3 x plus 5 right parenthesis plus 2  equals 9 x squared plus 30 x plus 25 minus 12 x minus 20 plus 2  equals 9 x squared plus 18 x plus 7

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Roboguru

Diketahui fungsi f:R→R dengan f(x)=x2−4x+2 dan fungsi g:R→R dengan g(x)=3x−7. Tentukanlah b)   f∘g d)   (f∘g)(10)

Pembahasan Soal:

a)  Subtitusikan g open parentheses x close parentheses pada f open parentheses x close parentheses.

table attributes columnalign right center left columnspacing 0px end attributes row cell f ring operator g open parentheses x close parentheses end cell equals cell f open parentheses g open parentheses x close parentheses close parentheses end cell row blank equals cell f open parentheses 3 x minus 7 close parentheses end cell row blank equals cell open parentheses 3 x minus 7 close parentheses squared minus 4 open parentheses 3 x minus 7 close parentheses plus 2 end cell row blank equals cell 9 x squared minus 42 x plus 49 minus 12 x plus 28 plus 2 end cell row blank equals cell 9 x squared minus 54 x plus 79 end cell end table 

d)  Maka nilai dari open parentheses f ring operator g close parentheses open parentheses 10 close parentheses

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses open parentheses 10 close parentheses end cell equals cell 9 x squared minus 54 x plus 79 end cell row blank equals cell 9 open parentheses 10 close parentheses squared minus 54 open parentheses 10 close parentheses plus 79 end cell row blank equals cell 900 minus 540 plus 79 end cell row blank equals 439 end table 

Jadi, Error converting from MathML to accessible text. dan table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses f ring operator g close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses 10 close parentheses 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 439 end table.

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Roboguru

Diketahui f(x)=x2+4x+4 dan g(x)=x2−4x+4. Rumus f(g(x))​+g(f(x))​=....

Pembahasan Soal:

Diketahui  dan . Rumus  

kita sederhanakan dulu fungsinya,

 = begin mathsize 14px style open parentheses x plus 2 close parentheses squared end style 

 = begin mathsize 14px style open parentheses x minus 2 close parentheses squared end style 

kemudian tentukan dulu fungsi komposisinya:

size 14px f size 14px left parenthesis size 14px g size 14px left parenthesis size 14px x size 14px right parenthesis size 14px right parenthesis size 14px equals size 14px f size 14px left parenthesis size 14px left parenthesis size 14px x size 14px minus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px left parenthesis size 14px x size 14px minus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px plus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px equals begin mathsize 14px style left parenthesis x squared minus 4 x plus 4 plus 2 right parenthesis end style to the power of size 14px 2 size 14px equals begin mathsize 14px style left parenthesis x squared minus 4 x plus 6 right parenthesis end style to the power of size 14px 2 size 14px g size 14px left parenthesis size 14px f size 14px left parenthesis size 14px x size 14px right parenthesis size 14px right parenthesis size 14px equals size 14px g size 14px left parenthesis size 14px left parenthesis size 14px x size 14px plus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px right parenthesis size 14px equals size 14px left parenthesis size 14px left parenthesis size 14px x size 14px plus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px minus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px equals begin mathsize 14px style left parenthesis x squared plus 4 x plus 4 minus 2 right parenthesis end style to the power of size 14px 2 size 14px equals size 14px left parenthesis size 14px x to the power of size 14px 2 size 14px plus size 14px 4 size 14px x size 14px plus size 14px 2 size 14px right parenthesis to the power of size 14px 2 size 14px space  square root of size 14px f size 14px left parenthesis size 14px g size 14px left parenthesis size 14px x size 14px right parenthesis size 14px right parenthesis end root size 14px plus square root of size 14px g size 14px left parenthesis size 14px f size 14px left parenthesis size 14px x size 14px right parenthesis size 14px right parenthesis end root size 14px equals square root of begin mathsize 14px style left parenthesis x squared minus 4 x plus 6 right parenthesis squared end style end root size 14px plus square root of size 14px left parenthesis size 14px x to the power of size 14px 2 size 14px plus size 14px 4 size 14px x size 14px plus size 14px 2 size 14px right parenthesis to the power of size 14px 2 end root size 14px equals size 14px x to the power of size 14px 2 size 14px minus size 14px 4 size 14px x size 14px plus size 14px 6 size 14px plus size 14px x to the power of size 14px 2 size 14px plus size 14px 4 size 14px x size 14px plus size 14px 2 size 14px equals size 14px 2 size 14px x to the power of size 14px 2 size 14px plus size 14px 8

jadi, jawabannya C

 

 

0

Roboguru

Jikaf(x)=x2−42x​dang(x)=2x​maka(fog)(x)=...

Pembahasan Soal:

f left parenthesis x right parenthesis equals fraction numerator 2 x over denominator x squared minus 4 end fraction  g left parenthesis x right parenthesis equals square root of 2 x end root  left parenthesis f o g right parenthesis left parenthesis x right parenthesis equals fraction numerator 2 open parentheses square root of 2 x end root close parentheses over denominator open parentheses square root of 2 x end root close parentheses squared minus 4 end fraction  left parenthesis f o g right parenthesis left parenthesis x right parenthesis equals fraction numerator 2 open parentheses square root of 2 x end root close parentheses over denominator x minus 2 end fraction

0

Roboguru

a. Jika  dan , tentukan (f∘g)(x).

Pembahasan Soal:

Ingat kembali komposisi dua fungsi:

(fg)(x)=f(g(x)) 

sehingga:

(fg)(x)(fg)(x)========f(g(x))f(x+242x)x+242x32(x+242x)+1x+2(42x)3(x+2)x+22(42x)+(x+2)42x3x684x+x+25x23x+101(5x+2)1(3x10)5x+23x10 

Dengan demikian, hasil dari  begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses end style  adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 x minus 10 over denominator 5 x plus 2 end fraction end cell end table. end style 

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Roboguru

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