Answer: [tex]f^{-1}(x)=\frac{x}{5}[/tex]
Step-by-step explanation:
By definition the domain of an inverse function [tex]f^-1(x)[/tex] is the range of f(x) and the range of the inverse function is equal to the domain of the principal function f(x).
If you have a function [tex]f(x)=5x[/tex], then to find the inverse function, follow these steps:
1. Make [tex]y=f(x)[/tex]
[tex]f(x)=y=5x[/tex]
[tex]y=5x[/tex]
2. Solve for the variable "x":
[tex]x=\frac{y}{5}[/tex]
3. Exchange the variable "x" with the variable "y":
[tex]y=\frac{x}{5}[/tex]
4. Exchange "y" with[tex]f^{-1}(x)[/tex]. Then the inverse function is:
[tex]f^{-1}(x)=\frac{x}{5}[/tex]
