Question

Find the inverse function of (x+1)/x

Answer 1

The domain of the function $f(x)=\frac{x+1}{x}$ consists of all real numbers except of . I.e., the domain is: $(-\infty,0)\cup(0,+\infty)$. In order to find the inverse, we need to solve the equation: $z=\frac{x+1}{x}$. We get: $zx=x+1$. We receive: $x=\frac{1}{z-1}$. The domain of the inverse function is: $(-\infty,1)\cup(1,+\infty)$

Answer: the inverse function is: $\frac{1}{z-1}$.