Question

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

Answer 1

Starting with the expression:

$f(x)=\frac{2}{1+2x}$

Substitute f(x)=y and isolate x:

$\begin{gathered} y=\frac{2}{1+2x} \\ \Rightarrow1+2x=\frac{2}{y} \\ \Rightarrow2x=\frac{2}{y}-1 \\ \Rightarrow x=\frac{1}{y}-\frac{1}{2} \end{gathered}$

Swap x for y and vice versa:

$y=\frac{1}{x}-\frac{1}{2}$

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

$f^{-1}(x)=\frac{1}{x}-\frac{1}{2}$