The definition of the inverse function states that
[tex]f^{-1}(f(x))=x[/tex]
Therefore,
[tex]\Rightarrow f^{-1}(\frac{1}{2}x+2)=x[/tex]
To transform x/2+2 into x we need to follow the steps below
1. Subtract -2 to obtain x/2
2. Multiply by 2 to obtain x.
Therefore, the inverse function is
[tex]f^{-1}(x)=2(x-2)[/tex]
If this is indeed the answer, it has to satisfy the identity above,
[tex]\begin{gathered} f^{-1}(\frac{1}{2}x+2)=2((\frac{1}{2}x+2)-2)=2(\frac{1}{2}x)=x \\ \Rightarrow f^{-1}(\frac{1}{2}x+2)=x \end{gathered}[/tex]
Therefore, the answer is
[tex]f^{-1}(x)=2(x-2)=2x-4[/tex]
The answer is 2x-4
