What is the inverse of f(x)=5(x+10)^{1/3}-8 ?

The inverse of f(x)=5(x+10)^{1/3}-8 is (x^3+24x^2+192x+512)/(125)-10

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inverse of f(x)=5(x+10)^{1/3}-8

inverse

f (x) = 5 (x + 10)^{\frac{1}{3}} - 8

\frac{x ^{3} + 24 x ^{2} + 192 x + 512}{125} - 10

Solution steps

y = 5 (x + 10)^{\frac{1}{3}} - 8

Replace

x

with

y

x = 5 (y + 10)^{\frac{1}{3}} - 8

Solve for

y, x = 5 (y + 10)^{\frac{1}{3}} - 8

\frac{x ^{3} + 24 x ^{2} + 192 x + 512}{125} - 10

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

y = 2 x^{2} - 5 x

5 x^{2} + 5 x

f (x) = 3 x^{2} - 4.03

\frac{x - 3}{x ^{2} - 3 x - 18}

What is the inverse of f(x)=5(x+10)^{1/3}-8 ?
The inverse of f(x)=5(x+10)^{1/3}-8 is (x^3+24x^2+192x+512)/(125)-10