Final answer:
To find the composition f(g(x)), we substitute g(x) into f(x). The composition f(g(x)) when f(x)=3x^2+2 and g(x)=2x+3 is 12x^2 + 36x + 29.
Step-by-step explanation:
The question involves forming the composition of two functions. In mathematical terms, composing two functions f(x) and g(x) means you're finding f(g(x)). This requires substituting g(x) into the function f(x).
Let's find the composition f(g(x)) when f(x) = 3x^2 + 2 and g(x) = 2x + 3. First, we'll substitute g(x) into f(x):
f(g(x)) = f(2x + 3) = 3(2x + 3)^2 + 2.
We then expand the bracket:
3(2x + 3)^2 + 2 = 3(4x^2 + 12x + 9) + 2
= 12x^2 + 36x + 27 + 2
= 12x^2 + 36x + 29.
So, the composition f(g(x)) is 12x^2 + 36x + 29.