Pertanyaan

Jika f ( x ) = x + 1 x , g ( x ) = x x − 1 dengan x  = 0 maka ( f ∘ g ) − 1 ( x ) adalah ....

Jika $f (x) = \frac{x}{x + 1}, g (x) = \frac{x - 1}{x} dengan x \neq = 0 maka (f \circ g)^{- 1} (x)$ adalah ....

$fraction numerator 1 minus straight x over denominator 1 minus 2 straight x end fraction$
$fraction numerator negative 1 over denominator straight x end fraction$
$fraction numerator 1 minus 2 straight x over denominator 1 minus straight x end fraction$
$fraction numerator 1 plus straight x over denominator 1 plus 2 straight x end fraction$

A. Acfreelance

Master Teacher

Mahasiswa/Alumni UIN Walisongo Semarang

Jawaban terverifikasi

Pembahasan

Mencari nilai sebelumnnya kita ubah terlebih dahulu ke invers Detelah mendapatkan invers dari f(x) dan g(x) maka yaitu Oleh karena itu jawabannya adalah D

Mencari nilai open parentheses straight f ring operator straight g close parentheses to the power of negative 1 end exponent open parentheses straight x close parentheses sebelumnnya kita ubah terlebih dahulu ke invers

$table attributes columnalign right center left columnspacing 0px end attributes row cell straight f open parentheses straight x close parentheses end cell equals cell fraction numerator straight x over denominator straight x plus 1 end fraction space end cell row cell straight f to the power of negative 1 end exponent open parentheses straight x close parentheses end cell equals cell fraction numerator negative dx plus straight b over denominator cx minus straight a end fraction end cell row cell straight f to the power of negative 1 end exponent open parentheses straight x close parentheses end cell equals cell fraction numerator negative 1 straight x plus 0 over denominator 1 straight x minus 1 end fraction end cell row blank equals cell fraction numerator negative straight x over denominator straight x minus 1 end fraction end cell row cell straight g open parentheses straight x close parentheses end cell equals cell fraction numerator straight x minus 1 over denominator straight x end fraction end cell row cell straight g to the power of negative 1 end exponent open parentheses straight x close parentheses end cell equals cell fraction numerator negative dx plus straight b over denominator cx minus straight a end fraction end cell row cell straight g to the power of negative 1 end exponent open parentheses straight x close parentheses end cell equals cell fraction numerator negative 0 straight x plus left parenthesis negative 1 right parenthesis over denominator 1 straight x minus 1 end fraction end cell row blank equals cell fraction numerator negative 1 over denominator straight x minus 1 end fraction space end cell end table$

Detelah mendapatkan invers dari f(x) dan g(x) maka open parentheses straight f ring operator straight g close parentheses to the power of negative 1 end exponent open parentheses straight x close parentheses yaitu

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses straight f ring operator straight g close parentheses to the power of negative 1 end exponent open parentheses straight x close parentheses end cell equals cell open parentheses g to the power of negative 1 end exponent ring operator f to the power of negative 1 end exponent close parentheses left parenthesis x right parenthesis end cell row blank equals cell fraction numerator negative open parentheses begin display style fraction numerator negative 1 over denominator x minus 1 end fraction end style close parentheses over denominator open parentheses begin display style fraction numerator negative 1 over denominator x minus 1 end fraction end style close parentheses minus 1 end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 1 over denominator x plus 1 end fraction end style over denominator begin display style fraction numerator 1 over denominator x minus 1 end fraction end style minus begin display style fraction numerator x minus 1 over denominator x minus 1 end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 1 over denominator x plus 1 end fraction end style over denominator begin display style fraction numerator 1 minus x minus 1 over denominator x minus 1 end fraction end style end fraction end cell row blank equals cell fraction numerator 1 over denominator x plus 1 end fraction cross times open parentheses fraction numerator x minus 1 over denominator negative x end fraction close parentheses end cell row blank equals cell fraction numerator 1 over denominator x plus 1 end fraction cross times fraction numerator x plus 1 over denominator x end fraction end cell row blank equals cell 1 over x end cell end table$

Oleh karena itu jawabannya adalah D

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