What is the inverse of f(x)=2x^{1/5}-4 ?

The inverse of f(x)=2x^{1/5}-4 is (x^5}{32}+\frac{5x^4)/8+5x^3+20x^2+40x+32

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inverse of f(x)=2x^{1/5}-4

inverse

\frac{x ^{5}}{32} + \frac{5 x ^{4}}{8} + 5 x^{3} + 20 x^{2} + 40 x + 32

Solution steps

y = 2 x^{\frac{1}{5}} - 4

Replace

x

with

y

x = 2 y^{\frac{1}{5}} - 4

Solve for

y, x = 2 y^{\frac{1}{5}} - 4

\frac{x ^{5}}{32} + \frac{5 x ^{4}}{8} + 5 x^{3} + 20 x^{2} + 40 x + 32

What is the inverse of f(x)=2x^{1/5}-4 ?
The inverse of f(x)=2x^{1/5}-4 is (x^5}{32}+\frac{5x^4)/8+5x^3+20x^2+40x+32