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

The inverse of f(x)= 1/2 x^{3/2} is 4^{1/3}x^{2/3}

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

f (x) = (x + 1)^{2}

(0, - 3), (6, 3)

f (x) = ln (x - x^{2})

- 2 x + 3 y = - 4, (1, 3)

f (x) = 4.71238898

What is the inverse of f(x)= 1/2 x^{3/2} ?
The inverse of f(x)= 1/2 x^{3/2} is 4^{1/3}x^{2/3}