What is the inverse of f(x)=\sqrt[5]{x^3-5}-1 ?

The inverse of f(x)=\sqrt[5]{x^3-5}-1 is cube root of x^5+5x^4+10x^3+10x^2+5x+6

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inverse of f(x)=\sqrt[5]{x^3-5}-1

inverse

f (x) = 5 x^{3} - 5 - 1

3 x^{5} + 5 x^{4} + 10 x^{3} + 10 x^{2} + 5 x + 6

Solution steps

y = 5 x^{3} - 5 - 1

Replace

x

with

y

x = 5 y^{3} - 5 - 1

Solve for

y, x = 5 y^{3} - 5 - 1

3 x^{5} + 5 x^{4} + 10 x^{3} + 10 x^{2} + 5 x + 6

f (x) = 6 - 3 x^{3}

2646 x^{142}

y = - 3 x - 5

x^{2} - x - 6

f (x) = x - 8 + 5

What is the inverse of f(x)=\sqrt[5]{x^3-5}-1 ?
The inverse of f(x)=\sqrt[5]{x^3-5}-1 is cube root of x^5+5x^4+10x^3+10x^2+5x+6