BAB KOMPOSISI DAN INVERS FUNGSI SOAL (g ○ f) (x) = ( 2f(x) - 1 ) / ( f(x) ) f (x - 1) = g( x ) DITANYA f ( x ) = ? f invers ( 3 ) = ? mohon disertai

Komposisi dan fungsi invers

f(x) = (2x + 1)/(x +1)
f⁻¹ (3) = - 2

[tex]\displaystyle (g\circ f)(x)=\frac{2f(x)-1}{f(x)}\\g(f(x))=\frac{2f(x)-1}{f(x)}\\g(x)=\frac{2x-1}{x}\\\\f(x-1)=g(x)\\f(x-1)=\frac{2x-1}x\\f(x-1+1)=\frac{2(x+1)-1}{x+1}\\f(x)=\frac{2x+2-1}{x+1}\\f(x)=\frac{2x+1}{x+1}\\\\y=\frac{2x+1}{x+1}\\y(x+1)=2x+1\\yx+y=2x+1\\yx-2x=1-y\\x(y-2)=1-y\\x=\frac{1-y}{y-2}\\\boxed{\boxed{f^{-1}(x)=\frac{1-x}{x-2}}}\\\\f^{-1}(3)=\frac{1-3}{3-2}\\\boxed{\boxed{f^{-1}(3)=-2}}[/tex]