What is the inverse of 10x^{1/5}-2 ?

The inverse of 10x^{1/5}-2 is (x^5)/(100000)+(x^4)/(10000)+(x^3)/(2500)+(x^2)/(1250)+x/(1250)+1/3125

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inverse of 10x^{1/5}-2

inverse

10 x^{\frac{1}{5}} - 2

\frac{x ^{5}}{100000} + \frac{x ^{4}}{10000} + \frac{x ^{3}}{2500} + \frac{x ^{2}}{1250} + \frac{x}{1250} + \frac{1}{3125}

Solution steps

y = 10 x^{\frac{1}{5}} - 2

Replace

x

with

y

x = 10 y^{\frac{1}{5}} - 2

Solve for

y, x = 10 y^{\frac{1}{5}} - 2

\frac{x ^{5}}{100000} + \frac{x ^{4}}{10000} + \frac{x ^{3}}{2500} + \frac{x ^{2}}{1250} + \frac{x}{1250} + \frac{1}{3125}

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

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

f (x) = \frac{x ^{2} - 3 x}{x}

f (x) = (x + 5)^{2} - 8

x - 4 + 2

What is the inverse of 10x^{1/5}-2 ?
The inverse of 10x^{1/5}-2 is (x^5)/(100000)+(x^4)/(10000)+(x^3)/(2500)+(x^2)/(1250)+x/(1250)+1/3125