f(x)= -x^2 + 10 find the inverse

1. Start from the original function:
y = -x^2 + 10

2. Switch \( x \) and \( y \):
x = -y^2 + 10

3. Solve for \( y \):
y^2 = 10 - x
y = \pm \sqrt{10 - x}

4. Restrict the domain of the original function \( f(x) \) to ensure it is one-to-one. For \( x \geq 0 \):
f^{-1}(x) = \sqrt{10 - x}

So the inverse function for the specified domain is:
f^{-1}(x) = \sqrt{10 - x}