Question

obtenha a inversa da função: f(x) =   x - 2       
                                                         x + 3

Answer 1

$Resolu\c{c}\~ao\to \left\{\begin{array}{ccc}f(x) = \frac{x-2}{x+3} \\\\y = \frac{x-2}{x+3}\\\\ x = \frac{y-2}{y+3} \\\\x*(y+3) = y-2\\\\xy+3x = y-2\\\\xy-y = -2-3x\\\\y(x-1) = -2-3x\\\\ \boxed{y = \frac{-3x-2}{x-1} } \end{array}\right$

$Resposta \to f^{-1}(x) \to \boxed{y = \frac{-3x-2}{x-1} }$

Espero ter ajudado. :))