What is the inverse of f(x)= 1/3 x^{3/2} ?

The inverse of f(x)= 1/3 x^{3/2} is 9^{1/3}x^{2/3}

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inverse of f(x)= 1/3 x^{3/2}

inverse

f (x) = \frac{1}{3} x^{\frac{3}{2}}

9^{\frac{1}{3}} x^{\frac{2}{3}}

Solution steps

y = \frac{1}{3} x^{\frac{3}{2}}

Replace

x

with

y

x = \frac{1}{3} y^{\frac{3}{2}}

Solve for

y, x = \frac{1}{3} y^{\frac{3}{2}}

9^{\frac{1}{3}} x^{\frac{2}{3}}

What is the inverse of f(x)= 1/3 x^{3/2} ?
The inverse of f(x)= 1/3 x^{3/2} is 9^{1/3}x^{2/3}