What is the inverse of f(x)=-2/5 (x-2)^3-4 ?

The inverse of f(x)=-2/5 (x-2)^3-4 is -\sqrt[3]{(5x+20)/2}+2

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inverse of f(x)=-2/5 (x-2)^3-4

inverse

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

Solution steps

y = - \frac{2}{5} (x - 2)^{3} - 4

Replace

x

with

y

x = - \frac{2}{5} (y - 2)^{3} - 4

Solve for

y, x = - \frac{2}{5} (y - 2)^{3} - 4

y = 3 (2)^{x} + 1

f (x) = \frac{x - 8}{8 x + 3}

3 ln (x + 4)

y^{2} + 1

\frac{1}{3} (y^{2} + 2)^{\frac{3}{2}}

What is the inverse of f(x)=-2/5 (x-2)^3-4 ?
The inverse of f(x)=-2/5 (x-2)^3-4 is -\sqrt[3]{(5x+20)/2}+2