Question

Find the inverse of the following function. gx= 1/x-2

Answer 1

In order to find the inverse function of g(x) = 1/x - 2, we just need to switch g(x) for x and x for g-1(x), then we isolate the inverse function g-1(x):

$\begin{gathered} g(x)=\frac{1}{x}-2 \\ x=\frac{1}{g^{-1}(x)}-2 \\ \frac{1}{g^{-1}(x)}=x+2 \\ g^{-1}(x)=\frac{1}{x+2} \end{gathered}$

So the inverse function is g-1(x) = 1/(x+2)