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

The inverse of f(x)=2(x-1)^2 is sqrt(x/2)+1,-sqrt(x/2)+1

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

inverse

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

\frac{x}{2} + 1, - \frac{x}{2} + 1

Solution steps

y = 2 (x - 1)^{2}

Replace

x

with

y

x = 2 (y - 1)^{2}

Solve for

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

\frac{x}{2} + 1, - \frac{x}{2} + 1

f (x) = 5 cos (\frac{π}{4} x)

f (x) = - 4 x + 2

f (x) = x (9 - 2 x) (12 - 2 x)

y = - 4 x - 1

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