Answer: [tex]f^{-1}(4)=\frac{8}{5}[/tex]
Step-by-step explanation:
1. You need to find the Inverse function [tex]f^{-1}(x)[/tex]:
- Given the function f(x):
[tex]f(x) = 3x - \frac{4}{ 5}[/tex]
- Rewrite it with [tex]f(x)=y[/tex]:
[tex]y= 3x - \frac{4}{ 5}[/tex]
- Now you must solve for "x":
[tex]y+\frac{4}{ 5} = 3x\\\\(y+\frac{4}{ 5})(3)=x\\\\x=\frac{y}{3}+\frac{4}{15}[/tex]
- Now you must exchange the variables:
[tex]y=\frac{x}{3}+\frac{4}{15}[/tex]
- Then:
[tex]f^{-1}(x)=\frac{x}{3}+\frac{4}{15}[/tex]
2. Substitute [tex]x=4[/tex] into the Inverse function and then evaluate:
[tex]f^{-1}(4)=\frac{(4)}{3}+\frac{4}{15}\\\\f^{-1}(4)=\frac{8}{5}[/tex]
