What is the inverse of f(x)=(x^{1/4}-1)^5 ?

The inverse of f(x)=(x^{1/4}-1)^5 is x^{4/5}+4x^{3/5}+6x^{2/5}+4\sqrt[5]{x}+1

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inverse of f(x)=(x^{1/4}-1)^5

inverse

f (x) = (x^{\frac{1}{4}} - 1)^{5}

Solution steps

y = (x^{\frac{1}{4}} - 1)^{5}

Replace

x

with

y

x = (y^{\frac{1}{4}} - 1)^{5}

Solve for

y, x = (y^{\frac{1}{4}} - 1)^{5}

1 + \frac{1}{x}

f (x) = - \frac{1}{10} x^{5} + 5 x^{3}

f (x) = x^{\frac{11}{5}} + x^{\frac{6}{5}}

f (x) = x x + 5

y = \frac{( 6 x + 1 )}{( 3 x - 5 )}

What is the inverse of f(x)=(x^{1/4}-1)^5 ?
The inverse of f(x)=(x^{1/4}-1)^5 is x^{4/5}+4x^{3/5}+6x^{2/5}+4\sqrt[5]{x}+1