What is the inverse of f(x)=(x^{1/5}+9)^3 ?

The inverse of f(x)=(x^{1/5}+9)^3 is x^{5/3}-45x^{4/3}+810x-7290x^{2/3}+32805\sqrt[3]{x}-59049

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inverse of f(x)=(x^{1/5}+9)^3

inverse

f (x) = (x^{\frac{1}{5}} + 9)^{3}

Solution steps

y = (x^{\frac{1}{5}} + 9)^{3}

Replace

x

with

y

x = (y^{\frac{1}{5}} + 9)^{3}

Solve for

y, x = (y^{\frac{1}{5}} + 9)^{3}

- x + 3

y = x + 1

f (x) = 4 (3)^{x}

x + 3

f (x) = x^{6} e^{x} - 6

What is the inverse of f(x)=(x^{1/5}+9)^3 ?
The inverse of f(x)=(x^{1/5}+9)^3 is x^{5/3}-45x^{4/3}+810x-7290x^{2/3}+32805\sqrt[3]{x}-59049