What is the inverse of f(x)= 1/2 (x-4)^3 ?

The inverse of f(x)= 1/2 (x-4)^3 is \sqrt[3]{2}\sqrt[3]{x}+4

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inverse of f(x)= 1/2 (x-4)^3

inverse

f (x) = \frac{1}{2} (x - 4)^{3}

Solution steps

y = \frac{1}{2} (x - 4)^{3}

Replace

x

with

y

x = \frac{1}{2} (y - 4)^{3}

Solve for

y, x = \frac{1}{2} (y - 4)^{3}

2 x - x^{2}

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

x^{2} - 4

f (x) = - 5 x^{3} + 5 x

f (x) = \frac{x - 1}{x + 4}

What is the inverse of f(x)= 1/2 (x-4)^3 ?
The inverse of f(x)= 1/2 (x-4)^3 is \sqrt[3]{2}\sqrt[3]{x}+4