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}) \cdot (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} \cdot (y - 2)^{3}

- 32 3 x + 2

f (x) = 3 x - 6

y = 2 (x - 6) + 3

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

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

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

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