What is the inverse of f(x)=\sqrt[5]{2x-1}-1 ?

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

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inverse of f(x)=\sqrt[5]{2x-1}-1

inverse

f (x) = 5 2 x - 1 - 1

\frac{x ^{5} + 5 x ^{4} + 10 x ^{3} + 10 x ^{2} + 5 x + 2}{2}

Solution steps

y = 5 2 x - 1 - 1

Replace

x

with

y

x = 5 2 y - 1 - 1

Solve for

y, x = 5 2 y - 1 - 1

\frac{x ^{5} + 5 x ^{4} + 10 x ^{3} + 10 x ^{2} + 5 x + 2}{2}

\frac{x ^{2} - 4}{x - 2}

\frac{tan ( x )}{sin ( x )}

y = x^{4} + 58 x^{3} + 5

y = 3 x + 5

f (x) = \frac{x ^{2} + 9}{x ^{2} - 2 x - 1}

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