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

The inverse of f(x)=x^{2/3}+9 is sqrt(x^3-27x^2+243x-729),-sqrt(x^3-27x^2+243x-729)

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inverse of f(x)=x^{2/3}+9

inverse

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

x^{3} - 27 x^{2} + 243 x - 729, - x^{3} - 27 x^{2} + 243 x - 729

Solution steps

y = x^{\frac{2}{3}} + 9

Replace

x

with

y

x = y^{\frac{2}{3}} + 9

Solve for

y, x = y^{\frac{2}{3}} + 9

x^{3} - 27 x^{2} + 243 x - 729, - x^{3} - 27 x^{2} + 243 x - 729

What is the inverse of f(x)=x^{2/3}+9 ?
The inverse of f(x)=x^{2/3}+9 is sqrt(x^3-27x^2+243x-729),-sqrt(x^3-27x^2+243x-729)