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

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

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

inverse

f (x) = e^{\frac{x}{3}}

9 ln^{2} (x)

Solution steps

y = e^{\frac{x}{3}}

Replace

x

with

y

x = e^{\frac{y}{3}}

Solve for

y, x = e^{\frac{y}{3}}

9 ln^{2} (x)

f (x) = 2 x^{3} + 3 x^{2} - 12 x + 1

f (x) = x + 5 y = 10

- \frac{1}{6} sin (6 x)

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

f (x) = \frac{x ^{2} - 9}{x + 3}

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