Final answer:
To find (f - g)(x), subtract function g(x) from f(x) and combine like terms. The resulting expression is -x² + 2x + 8.
Step-by-step explanation:
The expression (f - g)(x) represents the difference between the functions f(x) and g(x). To find this, we need to subtract the function g(x) from f(x). First, let's find f(x) - g(x):
f(x) - g(x) = (2x + 1) - (x² - 7)
Distributing the negative sign:
f(x) - g(x) = 2x + 1 - x² + 7
Combining like terms:
f(x) - g(x) = -x² + 2x + 8
Therefore, (f - g)(x) = -x² + 2x + 8.
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