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

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

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

inverse

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

- 32 3 x + 2

Solution steps

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

Replace

x

with

y

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

Solve for

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

- 32 3 x + 2

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

f (x) = (- 3 + 3)^{2} - 1

f (x) = \frac{3 x - 5}{6}

\frac{16}{x - 6}

x - \frac{4}{x}

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