Answer:
[tex]f^{-1}(x)= \frac{1}{2}x[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 2x[/tex]
Required:
Find [tex]f^{-1}(x)[/tex]
[tex]f(x) = 2x[/tex]
Replace f(x) with y
[tex]y = 2x[/tex]
Swap both variables
[tex]x = 2y[/tex]
[tex]2y = x[/tex]
Make y the subject
[tex]y= \frac{1}{2}x[/tex]
Replace y with f-1(x)
[tex]f^{-1}(x)= \frac{1}{2}x[/tex]
