, x ≤ 2
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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