Pertanyaan

Jika f ( x ) = 4 x + 6 , g ( x ) = x − 1 x ; x  = 1 , dan h ( x ) = ( f ∘ g ) ( x ) , invers fungsi h adalah...

Jika $f (x) = 4 x + 6, g (x) = \frac{x}{x - 1}; x \neq = 1, dan h (x) = (f \circ g) (x)$ , invers fungsi $h$ adalah...

$h to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator negative 5 x plus 6 over denominator 4 x minus 4 end fraction comma space x not equal to 1$
$h to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator negative 5 x minus 6 over denominator 4 x minus 4 end fraction comma space x not equal to 1$
$h to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x plus 6 over denominator x minus 10 end fraction comma space x not equal to 10$
$h to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x minus 6 over denominator x minus 10 end fraction comma space x not equal to 10$
$h to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x minus 10 over denominator x minus 6 end fraction comma space x not equal to 6$

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Z. Apriani

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Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Dengan menggunakan konsep invers fungsi komposisi: Misalkan , maka Oleh karena itu, jawaban yang benar adalah D.

Dengan menggunakan konsep invers fungsi komposisi:

$table attributes columnalign right center left columnspacing 0px end attributes row cell h left parenthesis x right parenthesis end cell equals cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell row blank equals cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell row blank equals cell 4 open parentheses fraction numerator x over denominator x minus 1 end fraction close parentheses plus 6 end cell row blank equals cell fraction numerator 4 x over denominator x minus 1 end fraction plus 6 end cell row blank equals cell fraction numerator 4 x over denominator x minus 1 end fraction plus fraction numerator 6 x minus 6 over denominator x minus 1 end fraction end cell row cell h left parenthesis x right parenthesis end cell equals cell fraction numerator 10 x minus 6 over denominator x minus 1 end fraction end cell end table$

Misalkan h left parenthesis x right parenthesis equals y , maka

$table attributes columnalign right center left columnspacing 0px end attributes row cell h left parenthesis x right parenthesis end cell equals y row y equals cell fraction numerator 10 x minus 6 over denominator x minus 1 end fraction end cell row cell y x minus y end cell equals cell 10 x minus 6 end cell row cell y x minus 10 x end cell equals cell y minus 6 end cell row cell x left parenthesis y minus 10 right parenthesis end cell equals cell y minus 6 end cell row x equals cell fraction numerator y minus 6 over denominator y minus 10 end fraction end cell row cell h apostrophe left parenthesis x right parenthesis end cell equals cell fraction numerator x minus 6 over denominator x minus 10 end fraction end cell end table$

Oleh karena itu, jawaban yang benar adalah D.