Question

For f(x) = 2x + 1 and g(x) = x² - 7, find (f - g)(x).

A. -x² - 6
B. 2x² - 15
C. -x² + 8
D. x² - 2x - 8

Answer 1

To find (f - g)(x), subtract g(x) from f(x) by combining like terms. The answer is option C. -x^2 + 2x + 8.

Step-by-step explanation:

To find (f - g)(x), we need to subtract g(x) from f(x). Let's substitute the given expressions for f(x) and g(x) into the equation:

(f - g)(x) = f(x) - g(x) = (2x + 1) - (x^2 - 7)

Next, distribute the negative sign to the terms in g(x) to get:

(f - g)(x) = 2x + 1 + (-x^2 + 7)

Combine like terms:

(f - g)(x) = -x^2 + 2x + 8

Therefore, the answer is C. -x^2 + 2x + 8.