What is the inverse of f(x)=5x^{1/3}+4 ?

The inverse of f(x)=5x^{1/3}+4 is (x^3)/(125)-(12x^2)/(125)+(48x)/(125)-64/125

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inverse of f(x)=5x^{1/3}+4

inverse

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

\frac{x ^{3}}{125} - \frac{12 x ^{2}}{125} + \frac{48 x}{125} - \frac{64}{125}

Solution steps

y = 5 x^{\frac{1}{3}} + 4

Replace

x

with

y

x = 5 y^{\frac{1}{3}} + 4

Solve for

y, x = 5 y^{\frac{1}{3}} + 4

\frac{x ^{3}}{125} - \frac{12 x ^{2}}{125} + \frac{48 x}{125} - \frac{64}{125}

f (x) = \frac{3 x - 9}{- 2 x + 3}

f (x) = 3 x^{0.3}

f (x) = - \frac{1}{6} cos (6 x)

(0, 0), (4, 0)

f (x) = \frac{x}{4} - 7

What is the inverse of f(x)=5x^{1/3}+4 ?
The inverse of f(x)=5x^{1/3}+4 is (x^3)/(125)-(12x^2)/(125)+(48x)/(125)-64/125