SOLUTION
[tex]f(x)=\frac{1}{2}x+\frac{1}{2}[/tex]To get the inverse, we first put y = f(x) then make x the subject, we have
[tex]\begin{gathered} f(x)=\frac{1}{2}x+\frac{1}{2} \\ y=\frac{1}{2}x+\frac{1}{2} \\ y-\frac{1}{2}=\frac{1}{2}x \end{gathered}[/tex]To remove the half fraction, multiply both sides of the equation by 2
[tex]\begin{gathered} 2y-2(\frac{1}{2})=2(\frac{1}{2}x) \\ 2y-1=x \\ x=2y-1 \end{gathered}[/tex]Now replace y with x and x with f(x) inverse, we have
[tex]f^{-1}(x)=2x-1[/tex]Hence the answer is
[tex]f^{-1}(x)=2x+(-1)[/tex]