What is the inverse of f(x)=2e^{3sqrt(x)} ?

The inverse of f(x)=2e^{3sqrt(x)} is (ln^2(x/2))/9

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inverse of f(x)=2e^{3sqrt(x)}

inverse

f (x) = 2 e^{3 x}

\frac{ln ^{2} ( \frac{x}{2} )}{9}

Solution steps

y = 2 e^{3 x}

Replace

x

with

y

x = 2 e^{3 y}

Solve for

y, x = 2 e^{3 y}

\frac{ln ^{2} ( \frac{x}{2} )}{9}

y = 0. 5^{x}

f (x) = \frac{x + 2}{2 x - 3}

f (x) = x - 2 - 3

- (\frac{1}{z ^{- 1}} - \frac{1}{3})

f (x) = \frac{2}{5} x - \frac{1}{5}

What is the inverse of f(x)=2e^{3sqrt(x)} ?
The inverse of f(x)=2e^{3sqrt(x)} is (ln^2(x/2))/9