What is the inverse of f(x)= 3x-9

Gank asked Apr 15, 2022

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Gank asked Apr 15, 2022

by Gank

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14 votes

If
f^(-1)(x) is the inverse of
f(x) , then

$f\left(f^(-1)(x)\right) = x$

Given

f(x) = 3x-9

composing with the inverse function gives

$f\left(f^(-1)(x)\right) = 3f^(-1)(x) - 9 = x$

Solve for the inverse:

$3f^(-1)(x)-9 = x \\\\ 3f^(-1)(x) = x+9 \\\\ \boxed{f^(-1)(x) = \frac x3 + 3}$

InsaneCat answered Apr 20, 2022

3.2k points

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