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

The inverse of f(x)=-1/2 (x-3)^2+1 is sqrt(-2x+2)+3,-sqrt(-2x+2)+3

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

inverse

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

- 2 x + 2 + 3, - - 2 x + 2 + 3

Solution steps

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

Replace

x

with

y

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

Solve for

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

- 2 x + 2 + 3, - - 2 x + 2 + 3

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