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

Pertanyaan

Diketahui $\style{font-size:14px}{f(x)=3x-2}$ 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 $\style{font-size:14px}{{(g\;\circ\;f)}^{-1}(x+3)=}$ ...

$begin mathsize 14px style fraction numerator negative 2 x minus 9 over denominator 3 x plus 3 end fraction comma space x not equal to negative 1 end style$
$begin mathsize 14px style fraction numerator negative 2 x minus 6 over denominator 3 x plus 3 end fraction comma space x not equal to negative 1 end style$
$begin mathsize 14px style fraction numerator 2 x minus 3 over denominator 3 x plus 9 end fraction comma space x not equal to negative 3 end style$
$begin mathsize 14px style fraction numerator 2 x plus 3 over denominator 3 x plus 9 end fraction comma space x not equal to negative 3 end style$
$begin mathsize 14px style fraction numerator negative 2 x minus 3 over denominator 3 x plus 9 end fraction comma space x not equal to negative 3 end style$

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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