What is the inverse of (9-x^{2/3})^{3/2} ?

The inverse of (9-x^{2/3})^{3/2} is (-\sqrt[3]{x^2}+9)^{3/2},-(-\sqrt[3]{x^2}+9)^{3/2}

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inverse of (9-x^{2/3})^{3/2}

inverse

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

Solution steps

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

Replace

x

with

y

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

Solve for

y, x = (9 - y^{\frac{2}{3}})^{\frac{3}{2}}

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

What is the inverse of (9-x^{2/3})^{3/2} ?
The inverse of (9-x^{2/3})^{3/2} is (-\sqrt[3]{x^2}+9)^{3/2},-(-\sqrt[3]{x^2}+9)^{3/2}