Solution :
Given , function[tex]f(x) = 2x+1[/tex]
we have to find the inverse of the function f(x)
Substitute y for f(x): [tex] y=2x+1[/tex]
Subtract 1 from both sides, [tex]y-1=2x+1-1[/tex]
Divide both sides by 2, [tex]\frac{y-1}{2} = x[/tex]
[tex]\Rightarrow x=\frac{y-1}{2}[/tex]
Substitute [tex]f^{-1}(y)\:for\:x [/tex][tex]\RIghtarrow f^{-1}(y)=\frac{y-1}{2}[/tex]
Hence, The inverse of the function [tex]f(x)=2x+1\:is f^{-1}(y)=\frac{y-1}{2}[/tex]
