Question

Find the inverse of f(x)=x/x+1

Answer 1

Given:

`f(x)=(x)/(x+1)`

For inverse function the value of x,y is interchange then solve for y :

`\begin{gathered} f(x)=y \\ y=(x)/(x+1) \\ x\rightarrow y \\ y\rightarrow x \end{gathered}`

`\begin{gathered} y=(x)/(x+1) \\ so\colon \\ x=(y)/(y+1) \\ x(y+1)=y \\ y=xy+x \\ y-xy=x \\ y(1-x)=x \\ y=(x)/(1-x) \end{gathered}`

So inverse function is:

`\begin{gathered} f(x)=(x)/(x+1) \\ f^(-1)(x)=(x)/(1-x) \end{gathered}`