Pertanyaan

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

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

$h to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator x minus 6 over denominator x minus 10 end fraction comma x not equal to 10$
$h to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator x plus 6 over denominator x minus 10 end fraction comma x not equal to 10$
$h to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator negative 5 x minus 6 over denominator 4 x minus 4 end fraction comma x not equal to 1$
$h to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator x minus 6 over denominator x minus 10 end fraction comma x not equal to negative 10$
$h to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator x minus 10 over denominator x minus 6 end fraction comma x not equal to 6$

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Dari soal diketahui Fungsi dapat ditentukan dengan caraberikut. Invers fungsi, merupakan fungsi kebalikan, sehingga Oleh karena itu, jawaban yang tepat adalah A.

Dari soal diketahui

$f open parentheses x close parentheses equals 4 x plus 6 g open parentheses x close parentheses equals fraction numerator x over denominator x minus 1 end fraction comma x not equal to 1$

Fungsi h open parentheses x close parentheses equals left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis dapat ditentukan dengan cara berikut.

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

Invers fungsi, merupakan fungsi kebalikan, sehingga h to the power of negative 1 end exponent open parentheses x close parentheses

$table attributes columnalign right center left columnspacing 0px end attributes row y equals cell fraction numerator 10 x minus 6 over denominator x minus 1 end fraction end cell row cell y x minus y end cell equals cell 10 x minus 6 end cell row cell y x minus 10 x end cell equals cell y minus 6 end cell row cell x open parentheses y minus 10 close parentheses end cell equals cell y minus 6 end cell row x equals cell fraction numerator y minus 6 over denominator y minus 10 end fraction end cell row cell h to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator x minus 6 over denominator x minus 10 end fraction comma x not equal to 10 end cell end table$

Oleh karena itu, jawaban yang tepat adalah A.