Determine the domain of composite function.?

Question

Suppose f(x)=x+2 and g(x)=square root x.
Determine the domain of the composite function g(f(x)).

Answer 1

g(f(x)) = sqrt(x+2)

so for domain you only need to find out when x+2>=0

So domain is: x>=-2, or [-2,infinitum)

Answer 2

The area of a composite function is the area of the interior (or proper) function, assuming the exterior function (left) doesn't impose extra regulations. (f o g)(x) = f(g(x)) = f(?(x)) = (?x)² do not simplify extra than that because you'll lose your area and ought to ought to state it explicitly, it extremely is tremendous, yet for the applications of this exercising i ought to point to leave it there till you recognize what the area is. it really is glaring that the area is x ? 0 from that with a view to say that that is a similar as x, x ? 0. It must be said explicitly because x ? (x, x ? 0). (g o f)(x) = g(f(x)) = g(x²) = ?(x²) again, stop there. And once again, really glaring that the area is ?, all reals. that is totally equivalent to |x|, absolutely the cost of x.

Answer 3

g(f(x)) = (x+2)^.5
The domain is [-2, infinity)
The function becomes imaginary if x < -2

Answer 4

gf(x) = sqrt(x+2) whose domain is [-2, infinity)