Question

Determine whether f has an inverse function. If it does, find the inverse function and state any restrictions on its domain. f(x)= (x-2) / (x+4)

Answer 1

\[f(x) = \frac{x-2}{x+4} \implies xf(x) + 4f(x) = x -2\]\[x(f(x) -1) = -2 - 4f(x) \implies x = \frac{4f(x) + 2}{1-f(x)}\]So, \[f^{-1}(x) = \frac{4x+2}{1-x}, x \epsilon R-\{1\}\]

Answer 2

Thank you so much! :)