What is the inverse of f(x)=(4x^5+1)^{1/9} ?

The inverse of f(x)=(4x^5+1)^{1/9} is \sqrt[5]{(x^9-1)/4}

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inverse of f(x)=(4x^5+1)^{1/9}

inverse

f (x) = (4 x^{5} + 1)^{\frac{1}{9}}

Solution steps

y = (4 x^{5} + 1)^{\frac{1}{9}}

Replace

x

with

y

x = (4 y^{5} + 1)^{\frac{1}{9}}

Solve for

y, x = (4 y^{5} + 1)^{\frac{1}{9}}

f (x) = (7 x + 14)^{\frac{1}{2}}

9 x^{3} - 54 x^{2} + 81 x + 13

y + 3 x - 5 = 0

\frac{d}{x d x}

f (x) = 4 x^{4} - 8 x^{3} + 4

What is the inverse of f(x)=(4x^5+1)^{1/9} ?
The inverse of f(x)=(4x^5+1)^{1/9} is \sqrt[5]{(x^9-1)/4}