What is the inverse of f(x)=2-3log_4(x+1) ?

Jun 12, 2018

${f}^{- 1} \left(x\right) = {4}^{\frac{2 - x}{3}} - 1$

Explanation:

We have
$3 {\log}_{4} \left(x + 1\right) = 2 - y$
${\log}_{4} \left(x + 1\right) = \frac{2 - y}{3}$
so ${4}^{\frac{2 - y}{3}} = x + 1$
so

$x = {4}^{\frac{2 - y}{3}} - 1$
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