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HELP functions

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2 Answers

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)=2x-3 and g(x)=√4x+3
find (f ° g)(x)
f(x)=2x-3
(f ° g)(x)=2(√4x+3)-3
I am assuming we are square-rooting 4x+3, not just 4x.  If not, please let me know.
Find the domain of (f ° g)(x)
As you already know, a square-rooted number must be equal to or greater than zero.
So...
4x+3≥0
Let's subtract 3 from both sides...
4x+3-3≥0-3
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 square-rooting 4x+3, not just 4x.  If not, please let me know.
f(x)=2x-3
(g ° f)(x)=√(4(2x-3)+3)
Let's simplify.
(g ° f)(x)=√8x-12+3
(g ° f)(x)=√8x-9
Find the domain of (g ° f)(x)
We cannot square root a negative number.
Therefore,
8x-9≥0
8x≥9
x≥9/8
The domain is...
(9/8, ∞)


(Fog) is f of g which means use g as your x value in your f(x) equation
 
same goes for (gof) use f(x) as your x value in the g(x) equation
 
your domain is every number that can possibly be the value of x