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

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

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

inverse

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

f (x) = 3 y + 5 x = 18

f (x) = 3 x - 7

f (x) = 10 x^{6}, x \leq 0

y = 3 x - 4

6 x^{3} - 5

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