Question

F(x)=2x-4. F(x)=2x-4 f-1x=_x+_. Complete the inverse function

Answer 1

Answer:

$f^{-1}(x) = \frac{1}{2}(x +4)$

Step-by-step explanation:

Given

$f(x) = 2x - 4$

Required

Determine the inverse function

Start by replacing f(x) with y

$y = 2x - 4$

Swap the positions of y and x

$x = 2y - 4$

Make y the subject: Add 4 to both sides

$x+4 = 2y - 4+4$

$x+4 = 2y$

Make y the subject: Divide through by 2

$\frac{1}{2}(x + 4) = y$

$y = \frac{1}{2}(x + 4)$

Replace y with f-1(x)

$f^{-1}(x) = \frac{1}{2}(x +4)$