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

The inverse of f(x)= 1/2 (x-1)^3+3 is \sqrt[3]{2x-6}+1

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

inverse

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

y = x^{3} + 3 x^{2} + 3 x + 2

y = \frac{1}{4} x

f (x) = 3 x - 1

f (x) = ln (6 x^{2} - 6 x - 11)

y = \frac{1}{3} x - 1

What is the inverse of f(x)= 1/2 (x-1)^3+3 ?
The inverse of f(x)= 1/2 (x-1)^3+3 is \sqrt[3]{2x-6}+1