Pertanyaan

Diketahui f ( x ) = 4 x + 2 dan g ( x ) = x + 1 x − 3 , x  = − 1. Invers dari ( g ∘ f ) ( x ) adalah ...

Diketahui
$f (x) = 4 x + 2 dan g (x) = \frac{x - 3}{x + 1}, x \neq = - 1. Invers dari (g \circ f) (x) adalah ...$

A. Septianingsih

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Pembahasan

Mencari invers :

Mencari invers :

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell fraction numerator 4 x minus 1 over denominator 4 x plus 3 end fraction end cell row y equals cell fraction numerator 4 x minus 1 over denominator 4 x plus 3 end fraction end cell row cell 4 x y minus 3 y end cell equals cell 4 x minus 1 end cell row cell 4 x y minus 4 x end cell equals cell 3 y minus 1 end cell row cell left parenthesis 4 y minus 4 right parenthesis x end cell equals cell 3 y minus 1 end cell row x equals cell fraction numerator 3 y minus 1 over denominator 4 y minus 4 end fraction end cell row blank blank blank row blank blank cell Maka space end cell row blank blank cell left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 3 x minus 1 over denominator 4 x minus 4 end fraction end cell end table end style$