Answer:
[tex]f^{-1}(x)=4x+20[/tex]
Step-by-step explanation:
Given
[tex]f(x)=\frac{x}{4}-5\\ \\y=\frac{x}{4}-5[/tex]
Swap x and y and solve for y
[tex]y=\frac{x}{4}-5\\ \\x=\frac{y}{4}-5\\ \\x+5=\frac{y}{4}\\ \\4(x+5)=y\\\\y=4x+20[/tex]
Final answer
[tex]f^{-1}(x)=4x+20[/tex]
Keep in mind that we need to swap the variables because a function and its inverse are symmetrical about the line y=x. See the graph below.
