Question

Determine a função inversa de f, de R – {5} em R – {-1}, definida por
f(x)= 6-x/x-5

Answer 1

Resposta:

$f(x)=\dfrac{6-x}{x-5}~~\to com~~x\neq 5~~~e~~y\neq -1$

Trocando as variáveis

$x=\dfrac{6-y}{y-5}~~\to com~~x\neq -1~~~e~~~y\neq 5\\ \\ \\ x(y-5)=6-y\\ \\ xy-5x=6-y\\ \\ isolando~~y\\ \\ xy+y=5x+6\\ \\ y(x+1)=5x+6\\ \\ \\ y=\dfrac{5x+6}{x+1}\\ \\\\ \boxed{ f^{-1}(x)=\dfrac{5x+6}{x+1}}$