Pertanyaan

Diketahui fungsi f : R → R dan g : R → R dengan f ( x ) = 2 x − 3 x dan g ( x ) = x + 5 , maka ( f ∘ g ) − 1 ( x ) = ...

Diketahui fungsi $f : R \to R$ dan $g : R \to R$ dengan $f (x) = \frac{x}{2 x - 3}$ dan $g (x) = x + 5$ , maka $(f \circ g)^{- 1} (x) = ...$

$fraction numerator x plus 5 over denominator 2 x plus 7 end fraction$
$fraction numerator 11 x minus 7 over denominator 2 x minus 3 end fraction$
$fraction numerator 3 x minus 7 over denominator 2 x minus 11 end fraction$
$fraction numerator negative 7 x plus 5 over denominator 2 x minus 3 end fraction$
$fraction numerator negative 7 x plus 5 over denominator 2 x minus 1 end fraction$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Oleh karena itu, jawaban yang benar adalah D.

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses left parenthesis x right parenthesis end cell equals cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell row blank equals cell fraction numerator x plus 5 over denominator 2 left parenthesis x plus 5 right parenthesis minus 3 end fraction end cell row blank equals cell fraction numerator x plus 5 over denominator 2 x plus 10 minus 3 end fraction end cell row blank equals cell fraction numerator x plus 5 over denominator 2 x plus 7 end fraction end cell row blank blank blank row blank blank cell open parentheses f ring operator g close parentheses to the power of negative 1 end exponent left parenthesis x right parenthesis equals y to the power of apostrophe end cell row cell y apostrophe end cell equals cell fraction numerator x plus 5 over denominator 2 x plus 7 end fraction end cell row cell y apostrophe open parentheses 2 x plus 7 close parentheses end cell equals cell x plus 5 end cell row cell 2 x y apostrophe minus x end cell equals cell negative 7 y plus 5 end cell row cell x left parenthesis 2 y apostrophe minus 1 right parenthesis end cell equals cell negative 7 y plus 5 end cell row x equals cell fraction numerator negative 7 y plus 5 over denominator 2 y apostrophe minus 1 end fraction end cell row cell open parentheses f ring operator g close parentheses to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator negative 7 x plus 5 over denominator 2 x minus 1 end fraction end cell row blank blank blank end table$

Oleh karena itu, jawaban yang benar adalah D.