Answer:
[tex]f^{-1}(x) = \frac{1}{2}(x +4)[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 2x - 4[/tex]
Required
Determine the inverse function
Start by replacing f(x) with y
[tex]y = 2x - 4[/tex]
Swap the positions of y and x
[tex]x = 2y - 4[/tex]
Make y the subject: Add 4 to both sides
[tex]x+4 = 2y - 4+4[/tex]
[tex]x+4 = 2y[/tex]
Make y the subject: Divide through by 2
[tex]\frac{1}{2}(x + 4) = y[/tex]
[tex]y = \frac{1}{2}(x + 4)[/tex]
Replace y with f-1(x)
[tex]f^{-1}(x) = \frac{1}{2}(x +4)[/tex]
