Question

Determine a inversa da função:
y=x+3/x-2

Answer 1

$y=\dfrac{x+3}{x-2}$

Substitua $y$ por $x$ e $x$ por $f^{-1}(x)$:

$x=\dfrac{f^{-1}(x)+3}{f^{-1}(x)-2}$

$x[f^{-1}(x)]-2x=f^{-1}(x)+3$

$x[f^{-1}(x)]-f^{-1}(x)=2x+3$

$f^{-1}(x)[x-1]=2x+3$

$f^{-1}(x)=\dfrac{2x+3}{x-1}$