Question

If `F(x) = sqrt 64 - x^2`, what is f(x)?

Answer 1

It your function is as shown, it would be `f(x)=-2x`

Because `root 2 64 = 8->F(x)=8-x^2`

But I think you meant `root 2 (64-x^2)= root 2 ((8+x)(8-x)`

Please confirm in a comment, before I go any further.

BTW :
We use the `f(x)->f'(x)` notation.
I hardly ever see the `F(x)->f(x)`