Diketahui f(x)=3x−2 dan g(x)=x+43​, x=−4, fungsi (g ∘ f)−1(x+3)= ...

Pertanyaan

Diketahui begin mathsize 14px style f left parenthesis x right parenthesis equals 3 x minus 2 end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals fraction numerator 3 over denominator x plus 4 end fraction comma space x not equal to negative 4 end style, fungsi begin mathsize 14px style left parenthesis g space ring operator space f right parenthesis to the power of negative 1 end exponent left parenthesis x plus 3 right parenthesis equals end style ...

  1. begin mathsize 14px style fraction numerator negative 2 x minus 9 over denominator 3 x plus 3 end fraction comma space x not equal to negative 1 end style 

  2. begin mathsize 14px style fraction numerator negative 2 x minus 6 over denominator 3 x plus 3 end fraction comma space x not equal to negative 1 end style 

  3. begin mathsize 14px style fraction numerator 2 x minus 3 over denominator 3 x plus 9 end fraction comma space x not equal to negative 3 end style 

  4. begin mathsize 14px style fraction numerator 2 x plus 3 over denominator 3 x plus 9 end fraction comma space x not equal to negative 3 end style 

  5. begin mathsize 14px style fraction numerator negative 2 x minus 3 over denominator 3 x plus 9 end fraction comma space x not equal to negative 3 end style 

F. Khansabyla

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Pembahasan

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 g open parentheses f open parentheses x close parentheses close parentheses end cell row blank equals cell g open parentheses 3 x minus 2 close parentheses end cell row blank equals cell fraction numerator 3 over denominator 3 x minus 2 plus 4 end fraction end cell row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell fraction numerator 3 over denominator 3 x plus 2 end fraction end cell end table end style 

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 y row y equals cell fraction numerator 3 over denominator 3 x plus 2 end fraction end cell row cell 3 x y plus 2 y end cell equals 3 row cell 3 x y end cell equals cell negative 2 y plus 3 end cell row x equals cell fraction numerator negative 2 y plus 3 over denominator 3 y end fraction end cell row cell open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator negative 2 x plus 3 over denominator 3 x end fraction end cell row cell open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x plus 3 close parentheses end cell equals cell fraction numerator negative 2 open parentheses x plus 3 close parentheses plus 3 over denominator 3 open parentheses x plus 3 close parentheses end fraction end cell row blank equals cell fraction numerator negative 2 x minus 6 plus 3 over denominator 3 x plus 9 end fraction end cell row cell open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x plus 3 close parentheses end cell equals cell fraction numerator negative 2 x minus 3 over denominator 3 x plus 9 end fraction end cell end table end style 

Jadi, jawaban yang tepat adalah E.
 

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Diketahui f(x)=x+2 dan g(x)=3x−10. Apakah (f−1∘g−1)(x)=(g∘f)−1(x)?  Sifat apa yang dapat kalian temukan dari fungsi invers pada komposisi?

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