We can calculate the inverse of a function y=f(x) by clearing x as x=g(y).
We have the function:
[tex]f(x)=\frac{1}{2}x-5[/tex]We can find the inverse as:
[tex]\begin{gathered} y=\frac{1}{2}x-5 \\ y+5=\frac{1}{2}x \\ 2(y+5)=x \\ x=2y+10 \end{gathered}[/tex]The inverse function is:
[tex]f^{-1}(x)=2x+10[/tex]Answer: f^-1(x)=2x+10
