, x ≤ 2

Hello!

To find the inverse function, f^(-1)(y), we have to solve for x the equation

y = f(x) = 2 - x^2.

It is simple:

x^2 = 2 - y,

x = f^(-1)(y) = sqrt(2-y).

Here y must be <=-2 and we choose +sqrt(2-y), not -sqrt(2-y), because it is given that x>=0.

answer is incorrect

Of course y<=2, not -2. But the formula for f^(-1) is correct, I see no error.

maybe you want y to be replaced by x,

f^(-1)(x) = sqrt(2-x) ?

sqrt is for square root

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