Here are the steps in getting the inverse of the given function:
1. Replace f(x) with y.
[tex]y=2x-7[/tex]
2. Switch x and y.
[tex]x=2y-7[/tex]
3. Isolate y.
Add 7 on both sides of the equation.
[tex]\begin{gathered} x+7=2y-7+7 \\ x+7=2y \end{gathered}[/tex]
Divide both sides of the equation by 2 to remove the 2 in 2y.
[tex]\frac{x+7}{2}=\frac{2y}{2}[/tex][tex]\frac{x+7}{2}=y[/tex]
4. Replace y with the symbol for the inverse of f(x).
[tex]f^{-1}(x)=\frac{x+7}{2}[/tex]
The inverse of the given function is (x + 7)/2 as shown above.
