Roboguru

Diketahui (f∘g)(x)=42x+1. Jika g(x)=2x−1, maka f(x)=....

Pertanyaan

Diketahui begin mathsize 14px style left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals 4 to the power of 2 x plus 1 end exponent end style. Jika begin mathsize 14px style g left parenthesis x right parenthesis equals 2 x minus 1 end style, maka begin mathsize 14px style f left parenthesis x right parenthesis equals end style....

  1.  begin mathsize 14px style 4 to the power of x plus 2 end exponent end style 

  2.  begin mathsize 14px style 4 to the power of 2 x plus 3 end exponent end style 

  3.  begin mathsize 14px style 4 to the power of 2 x plus 1 end exponent plus 1 half end style 

  4.  begin mathsize 14px style 2 to the power of 2 x plus 1 end exponent plus 1 half end style 

  5.  begin mathsize 14px style 2 to the power of 2 x plus 1 end exponent plus 1 end style 

Pembahasan Soal:

Kita mempunyai

begin mathsize 14px style left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals 4 to the power of 2 x plus 1 end exponent g left parenthesis x right parenthesis equals 2 x minus 1 end style 

Perhatikan perhitungan berikut!

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell 4 to the power of 2 x plus 1 end exponent end cell row cell left parenthesis f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell equals cell 4 to the power of 2 x plus 1 end exponent end cell row cell f left parenthesis 2 x minus 1 right parenthesis end cell equals cell 4 to the power of 2 x plus 1 end exponent end cell end table end style

Misal undefined, maka

 begin mathsize 14px style 2 x minus 1 equals a 2 x equals 1 plus a x equals fraction numerator a plus 1 over denominator 2 end fraction space end style  

Dengan demikian, kita mencari undefined.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis 2 x minus 1 right parenthesis end cell equals cell 4 to the power of 2 x plus 1 end exponent end cell row cell f left parenthesis a right parenthesis end cell equals cell 4 to the power of 2 left parenthesis fraction numerator a plus 1 over denominator 2 end fraction right parenthesis plus 1 end exponent end cell row cell f left parenthesis a right parenthesis end cell equals cell 4 to the power of a plus 1 plus 1 end exponent end cell row cell f left parenthesis a right parenthesis end cell equals cell 4 to the power of a plus 2 end exponent end cell end table end style

Jadi, kita peroleh begin mathsize 14px style f left parenthesis a right parenthesis equals 4 to the power of a plus 2 end exponent end style.

Dengan demikian, kita ubah begin mathsize 14px style a end style menjadi begin mathsize 14px style x end style sehingga diperoleh hasil perhitungan sebagai berikut.

begin mathsize 14px style f left parenthesis x right parenthesis equals 4 to the power of x plus 2 end exponent end style

Jadi, jawaban yang tepat adalah A.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Terakhir diupdate 05 Oktober 2021

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Pertanyaan yang serupa

Tentukan rumus fungsi f(x) jika diketahui (f∘g)(x)=4x+6 dan g(x)=2x+5

Pembahasan Soal:

Misalkan begin mathsize 14px style y equals 2 x plus 5 end style maka begin mathsize 14px style x equals fraction numerator y minus 5 over denominator 2 end fraction end style sehingga:

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 plus 6 end cell row cell f open parentheses g open parentheses x close parentheses close parentheses end cell equals cell 4 x plus 6 end cell row cell f open parentheses 2 x plus 5 close parentheses end cell equals cell 4 x plus 6 end cell row cell f open parentheses y close parentheses end cell equals cell 4 open parentheses fraction numerator y minus 5 over denominator 2 end fraction close parentheses plus 6 end cell row cell f open parentheses y close parentheses end cell equals cell 2 y minus 4 end cell end table end style 

Jadi, begin mathsize 14px style f open parentheses x close parentheses equals 2 x minus 4 end style.

0

Roboguru

Diketahui g(x)=x−1 dan (f∘g)(x)=x−12x−1​ , maka nilai dari f(2)=....

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell fraction numerator 2 x minus 1 over denominator x minus 1 end fraction end cell row cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell equals cell fraction numerator 2 x minus 1 over denominator x minus 1 end fraction end cell row cell f left parenthesis x minus 1 right parenthesis end cell equals cell fraction numerator 2 left parenthesis x minus 1 right parenthesis plus 1 over denominator left parenthesis x minus 1 right parenthesis end fraction end cell row cell f left parenthesis x right parenthesis end cell equals cell fraction numerator 2 x plus 1 over denominator x end fraction end cell row blank rightwards arrow cell f left parenthesis 2 right parenthesis equals fraction numerator 2 left parenthesis 2 right parenthesis plus factorial over denominator 2 end fraction end cell row blank equals cell fraction numerator 4 plus 1 over denominator 2 end fraction end cell row blank equals cell 5 over 2 end cell end table end style

Jadi, jawaban yang tepat adalah E.

0

Roboguru

Dari fungsi f dan g diketahui g(x)=x−1 dan . Jika f(a)=5, maka tentukan nilai a!

Pembahasan Soal:

Diketahui begin mathsize 14px style g open parentheses x close parentheses equals x minus 1 end style dan size 14px left parenthesis size 14px f size 14px ring operator size 14px g size 14px right parenthesis begin mathsize 14px style left parenthesis x right parenthesis end style size 14px equals size 14px 4 size 14px x to the power of size 14px 2 size 14px minus size 14px x

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px 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 x end cell blank row cell f open parentheses g open parentheses x close parentheses close parentheses end cell equals cell 4 x squared minus x end cell blank row cell f open parentheses x minus 1 close parentheses end cell equals cell 4 x squared minus x space end cell cell left square bracket m i s a l space s equals x minus 1 semicolon space x equals s plus 1 right square bracket end cell row cell f open parentheses s close parentheses end cell equals cell 4 open parentheses s plus 1 close parentheses squared minus open parentheses s plus 1 close parentheses end cell blank row cell f open parentheses s close parentheses end cell equals cell 4 open parentheses s squared plus 2 s plus 1 close parentheses minus s minus 1 end cell blank row cell f open parentheses s close parentheses end cell equals cell 4 s squared plus 7 s plus 3 end cell blank row cell f open parentheses x close parentheses end cell equals cell 4 x squared plus 7 x plus 3 end cell blank end table end style

Jika begin mathsize 14px style f open parentheses a close parentheses equals 5 end style, maka
begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell f open parentheses a close parentheses end cell equals cell 4 a squared plus 7 a plus 3 end cell row 5 equals cell 4 a squared plus 7 a plus 3 end cell row 0 equals cell 4 a squared plus 7 a minus 2 end cell row 0 equals cell open parentheses 4 a minus 1 close parentheses open parentheses a plus 2 close parentheses end cell row blank blank blank end table end style

Sehingga
begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell 4 a minus 1 end cell equals 0 row cell 4 a end cell equals 1 row a equals cell 1 fourth end cell end table end style

atau
begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell a plus 2 end cell equals 0 row a equals cell negative 2 end cell end table end style

Jadi nilai yang memenuhi adalah begin mathsize 14px style a equals negative 2 space atau space a equals 1 fourth end style 

 

0

Roboguru

Jika g(x)=x+1 dan (f∘g)(x)=2x−1 maka f(4)=....

Pembahasan Soal:

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 left parenthesis x right parenthesis close parentheses end cell row cell 2 x minus 1 end cell equals cell f left parenthesis x plus 1 right parenthesis end cell end table 

Misal y equals x plus 1 x equals y minus 1 

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x minus 1 end cell equals cell f left parenthesis x plus 1 right parenthesis end cell row cell 2 left parenthesis y minus 1 right parenthesis minus 1 end cell equals cell f left parenthesis y right parenthesis end cell row cell 2 y minus 2 minus 1 end cell equals cell f left parenthesis y right parenthesis end cell row cell 2 y minus 3 end cell equals cell f left parenthesis y right parenthesis end cell end table 

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis y right parenthesis end cell equals cell 2 y minus 3 end cell row cell f left parenthesis 4 right parenthesis end cell equals cell 2 left parenthesis 4 right parenthesis minus 3 end cell row blank equals cell 8 minus 3 end cell row blank equals 5 end table 

Jadi, nilai f left parenthesis 4 right parenthesis adalah 5.

0

Roboguru

Diketahui (g∘f)(x)=2x+1dang(x)=2x−3, tentukan nilai f(x).

Pembahasan Soal:

Diketahui begin mathsize 14px style open parentheses straight g ring operator straight f close parentheses open parentheses straight x close parentheses equals 2 straight x plus 1 space dan space straight g left parenthesis straight x right parenthesis equals 2 straight x minus 3 end style, maka

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

Jadi, jawaban yang tepat adalah A.

0

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