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Functions – Inverse Functions: Problem 9

If f(x)=(2x-8)/(5x+4), find the inverse function.

First we interchange x and y:

x=(2y-8)/(5y+4)

Next, we multiply both sides by 5y+4:

x(5y+4)=2y-8

Distribute the x:

5xy+4x=2y-8

Rearrange the terms:

4x+8=2y-5xy

Factor out y:

4x+8=(2-5x)y

Divide both sides by (2-5x):

(4x+8)/(2-5x)=y

Replace y with f^-1(x):

f^-1(x)=(4x+8)/(2-5x)