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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)
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