Step 1
Given;
[tex]y=4x-1[/tex]Required; To find
[tex]f^{-1}(7)[/tex]Step 2
Find the inverse of f(x)
Set x =y and y =x
[tex]x=4y-1[/tex]solve for y
[tex]\begin{gathered} 4y=x+1 \\ y=\frac{x+1}{4} \\ f^{-1}(x)=\frac{x+1}{4} \end{gathered}[/tex][tex]\begin{gathered} Find\text{ f}^{-1}(7) \\ \text{ f}^{-1}(7)=\frac{7+1}{4}=\frac{8}{4}=2 \\ \text{ f}^{-1}(7)=2 \end{gathered}[/tex]Answer;
[tex]\text{ f}^{-1}(7)=2[/tex]