Final answer:
To find the composition (f \circ g)(x), we substitute g(x) into f(x) and simplify the resulting expression. The functions given are f(x) = x^2 - 2x + 3 and g(x) = 2x + 1, resulting in the composition (f \circ g)(x) = 4x^2 + 1.
Step-by-step explanation:
To find (f \circ g)(x), which is the composition of the functions f(x) and g(x), you need to substitute g(x) into f(x). So, you will replace every instance of 'x' in f(x) with the function g(x).
Starting with the given functions f(x) = x2 - 2x + 3 and g(x) = 2x + 1, we proceed as follows:
- First, write down the expression for f(x) replacing x with g(x): f(g(x)) = (2x + 1)2 - 2(2x + 1) + 3.
- Simplify the expression by expanding and combining like terms:
- (2x + 1)2 = 4x2 + 4x + 1
- -2(2x + 1) = -4x - 2
- Now combine 4x2 + 4x + 1 - 4x - 2 + 3.
After combining the terms, you get f(g(x)) = 4x2 + 1.
Therefore, the composition (f \circ g)(x) is equal to 4x2 + 1.