What is the inverse of f(x)=(x^{1/3})/5+8 ?

The inverse of f(x)=(x^{1/3})/5+8 is 125x^3-3000x^2+24000x-64000

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inverse of f(x)=(x^{1/3})/5+8

inverse

f (x) = \frac{x ^{\frac{1}{3}}}{5} + 8

125 x^{3} - 3000 x^{2} + 24000 x - 64000

Solution steps

y = \frac{x ^{\frac{1}{3}}}{5} + 8

Replace

x

with

y

x = \frac{y ^{\frac{1}{3}}}{5} + 8

Solve for

y, x = \frac{y ^{\frac{1}{3}}}{5} + 8

125 x^{3} - 3000 x^{2} + 24000 x - 64000

(x + 2)^{3} - 8

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

f (x) = - \frac{1}{2} (x - 1)^{2} + 8

f (x) = x - 3 + 4

f (x) = - 3 x + 14

What is the inverse of f(x)=(x^{1/3})/5+8 ?
The inverse of f(x)=(x^{1/3})/5+8 is 125x^3-3000x^2+24000x-64000