Question

As funções reais definidas a seguir são bijetoras. Ache a fórmula da inversa  f^-1 de cada uma delas:

a)$f(x)= \frac{2x+1}x-3}$

b)$f(x)= \sqrt[3]{x} -8$

Answer 1

A)$f(x) = \frac{2x+1}{x-3}\\\\ y = \frac{2x+1}{x-3}\\\\ x = \frac{2y+1}{y-3}\\\\ x(y-3) = 2y+1\\\\ xy-3x = 2y+1\\\\ xy-2y = 3x+1\\\\ y(x-2) = 3x+1\\\\ y = \frac{3x+1}{x-2}\\\\ \boxed{f^-(x) = \frac{3x+1}{x-2}}$

B) $f(x) = \sqrt[3]{x} -8\\\\ y = \sqrt[3]{x}-8\\\\ x = \sqrt[3]{y}-8\\\\ \sqrt[3]{y} = x+8\\\\ y = \sqrt[3]{x+8}\\\\ \boxed{f^-(x) = \sqrt[3]{x+8}}$