Question

For the function f(x)=2/1+2x find f-1(x)

Answer 1

Starting with the expression:

`f(x)=(2)/(1+2x)`

Substitute f(x)=y and isolate x:

`\begin{gathered} y=(2)/(1+2x) \\ \Rightarrow1+2x=(2)/(y) \\ \Rightarrow2x=(2)/(y)-1 \\ \Rightarrow x=(1)/(y)-(1)/(2) \end{gathered}`

Swap x for y and vice versa:

`y=(1)/(x)-(1)/(2)`

Set y=f^{-1}(x):

`f^(-1)(x)=(1)/(x)-(1)/(2)`