So I have to find f of g which turns out to be

square root of (1 - (square root 1+ x)^2)

I can simplify this to square root of -x I believe.

Original f(x) = square root 1-x^2

Original g(x) = square root 1+x

Domain of f(x) = x less than or equal to 1

Domain of g(x) = x greater or equal to -1

Domain of f of g = x less than or equal to 0

The domain for square root of -x should then be [0,1] right?