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

The inverse of f(x)=(x^{1/5}+3)^3 is x^{5/3}-15x^{4/3}+90x-270x^{2/3}+405\sqrt[3]{x}-243

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

inverse

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

f (x) = \frac{2}{3 x - 4}

f (x) = \frac{3 x + 10}{7}

f (x) = 1 + ln (\frac{1 - x}{1 + x})

\frac{x ^{3} + 8}{7}

What is the inverse of f(x)=(x^{1/5}+3)^3 ?
The inverse of f(x)=(x^{1/5}+3)^3 is x^{5/3}-15x^{4/3}+90x-270x^{2/3}+405\sqrt[3]{x}-243