Hi Erica;
In the function of f(x), x is considered as x.
In the function of (f ° g)(x), x is considered as g(x).
This is about substitution.
f(x)=2x3 and g(x)=√4x+3
find (f ° g)(x)
f(x)=2x3
(f ° g)(x)=2(√4x+3)3
I am assuming we are squarerooting 4x+3, not just 4x. If not, please let me know.
Find the domain of (f ° g)(x)
As you already know, a squarerooted number must be equal to or greater than zero.
So...
4x+3≥0
Let's subtract 3 from both sides...
4x+33≥03
4x≥3
Let's divide both sides by 4.
4x/4≥3/4
x≥3/4
This domain of this equation is 3/4 to infinity.
domain=(3/4,∞)
In the equation of (g ° f)(x), x is considered as f(x)...
Find (g ° f)(x)
g(x)=√4x+3
As before, I am assuming that we are squarerooting 4x+3, not just 4x. If not, please let me know.
f(x)=2x3
(g ° f)(x)=√(4(2x3)+3)
Let's simplify.
(g ° f)(x)=√8x12+3
(g ° f)(x)=√8x9
Find the domain of (g ° f)(x)
We cannot square root a negative number.
Therefore,
8x9≥0
8x≥9
x≥9/8
The domain is...
(9/8, ∞)
10/7/2013

Vivian L.