We are given the following function:
[tex]f(x)=\frac{x-3}{2}[/tex]
We are asked to determine:
[tex]f^{-1}(x)[/tex]
This is called the inverse function.
To do that we will first switch the value of the variables f(x) and "x" as follows:
[tex]x=\frac{f(x)-3}{2}[/tex]
Now, we will solve for f(x). To do that we will multiply both sides by 2:
[tex]2x=f(x)-3[/tex]
Now we add 3:
[tex]2x+3=f(x)[/tex]
This is the inverse, therefore, we change:
[tex]f(x)=f^{-1}(x)[/tex]
Therefore, we have:
[tex]f^{-1}(x)=2x+3[/tex]
