SOLUTION: How do you solve this function of operations: Given:f(x) = x^2 - 4 (x squared minus 4) and g(x) = radical 2x + 4 Solve: Domain of f(g(x)) I understand that I have to plug in

Question 6671: How do you solve this function of operations:
Given:f(x) = x^2 - 4 (x squared minus 4) and g(x) = radical 2x + 4
Solve: Domain of f(g(x))
I understand that I have to plug in g(x) into f(x) but I don't understand the part about the Domain. Please help me. Thanks.

Answer by prince_abubu(198) (Show Source): You can put this solution on YOUR website!
I'm thinking that you meant . If you plug that into f(x), you'll get:

<---- The domain would have to be the set of values that you could plug into f(g(x)) legally. In other words, what values of x can we put into the function so that none of those values will make a denominator zero, or whatever inside the square root "house" negative. In this case, you can choose any x value you want, since you can multiply 2 times any number.

Say that you meant . If you plug that into f(x), you'll get:

<--- Used FOIL

<---- Simplified.

Now, what's the domain of f(g(x)) in that case? It would be all real numbers x greater than or equal to zero. You can't plug in negative numbers into that function because doing so will force the 2x inside to be a negative number, which you can't do inside square roots.

RELATED QUESTIONS
How do you find the domain of (g o f)(x) for f(x)=x/x-2 and g(x)=... (answered by jsmallt9)

Find the following and identify the domain: given f(x)= x - 2 and g(x)=x(squared)- 4 (answered by Nate)

Given f(x)= 3 over x(squared)-4 and g(x)= 5 over x Find the following 1. f o g... (answered by MathLover1)

3.14 Given f(x)=x-4 and g(x)=4x^2, find f+g, f-g, fg, and f/g. Determine the domain... (answered by ikleyn)

How do you find the domain of f. Given the function... (answered by solver91311,reviewermath)

How do you solve domains of functions? For example, f(x)=square root of (x-2)... (answered by lwsshak3)

How do you solve this? f(x)=x+1 and g(x)=2x f(g(x))= ? (answered by funmath)

Find the domain of the composite function f*g f(x)=4/x-2;g(x)=9/x The domain ____ (answered by josgarithmetic)

Please explain how to solve this: Let f(x) = 1/(x + 4) and g(x) = 8x/(x + 4) Find f... (answered by MathLover1)