function operations help please?

Question

If f(x) = (x^2)-4 and g(x) = √(2x+4), determine
1. f(3)
2. f(x) = 0 when x = ?
3. f(g(4))
4. f(g(x))
5. Domain of f(g(x))
6. g(f(0))
7. g(f(a+2))
8. f^-1(x)
9. Is the inverse of f(x) a function? If its not, how could the domain of f be restricted to make its inverse a function?

Thanks so much for the help in advance.

Answer 1

f(3) =5
2)x=+-2
g(4)=sqrt(12) so f(g(4)) = 8
f(g(x) ) = 2x
5) 2x+4>=0 so x>=-2
6)f(0)=-4 so g(-4) does not exist
7)f(a+2=)=a^2+2a+4-4= a^2+2a)
so g = sqrt(2a^2+4a+4)
8) is not a function x= +-sqrt(y+4)
9) domain of f(x) are all real numbers
for(8) f(x)>=-4 any x but the +- remains

Answer 2

1=5
2=+2,-2
3=8
4=2x
5={-2,infinity}
6=0 doesn't belong to domain of g(f(x))
7=root of 2a^2+8a
8=root of x+4
9=f(x) is not one to one it can be one to one by setting its domain {0,infinity}