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

The inverse of f(x)=4x^{1/5}+2 is (x^5)/(1024)-(5x^4)/(512)+(5x^3)/(128)-(5x^2)/(64)+(5x)/(64)-1/32

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

inverse

f (x) = 4 x^{\frac{1}{5}} + 2

\frac{x ^{5}}{1024} - \frac{5 x ^{4}}{512} + \frac{5 x ^{3}}{128} - \frac{5 x ^{2}}{64} + \frac{5 x}{64} - \frac{1}{32}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{x ^{5}}{1024} - \frac{5 x ^{4}}{512} + \frac{5 x ^{3}}{128} - \frac{5 x ^{2}}{64} + \frac{5 x}{64} - \frac{1}{32}

f (x) = 121 x^{2}

f (x) = 13 - x^{2}

f (x) = \frac{x + 3}{7}

f (x) = \frac{1}{3} (5)^{- 2 (x + 4)} - 1

f (x) = - 2 (x + 1)^{2} - 4

What is the inverse of f(x)=4x^{1/5}+2 ?
The inverse of f(x)=4x^{1/5}+2 is (x^5)/(1024)-(5x^4)/(512)+(5x^3)/(128)-(5x^2)/(64)+(5x)/(64)-1/32