ANSWER
[tex]f(x)\text{ = }\frac{x}{5}\text{ - }\frac{4}{5}[/tex]EXPLANATION
We have to find the inverse of:
[tex]f^{-1}(x)\text{ = 5x + 4}[/tex]First, replace f^(-1) (x) with x and replace x with y:
[tex]x\text{ = 5y + 4}[/tex]Now, make y the subject of the formula:
[tex]\begin{gathered} x\text{ - 4 = 5y} \\ \text{Divide through by 5:} \\ y\text{ = }\frac{x\text{ - 4}}{5}\text{ } \\ y\text{ = }\frac{x}{5}\text{ - }\frac{4}{5} \end{gathered}[/tex]Now, replace y with f(x):
[tex]f(x)\text{ = }\frac{x}{5}\text{ - }\frac{4}{5}[/tex]That is the inverse.
Note: The inverse of f^-1(x) is f(x).
