Question

Evaluate ((-3)) when (f(x) = 2x - 2) and (g(x) = 2x² + 14x + 5).

A. (8)
B. (19)
C. (2)
D. (19)

Answer 1

To evaluate ((-3)) for given functions f(x) and g(x), we substitute -3 into f(x) to find f(-3), then substitute f(-3) into g(x). The result of g(f(-3)) is 21, which is not among the provided options.

Step-by-step explanation:

To evaluate ((-3)) where f(x) is defined as f(x) = 2x - 2 and g(x) is defined as g(x) = 2x² + 14x + 5, we need to follow these steps:

• First, substitute x with -3 in f(x) to get f(-3) = 2(-3) - 2 = -6 - 2 = -8.
• Then, substitute x with -3 in g(x) to get g(-3) = 2(-3)² + 14(-3) + 5 = 2(9) - 42 + 5 = 18 - 42 + 5 = -19.
• The notation ((-3)) suggests we are evaluating g(f(-3)), which means substituting f(-3) into g(x). Thus, we have g(-8) = 2(-8)² + 14(-8) + 5.
• Finally, calculate g(-8) to get 2(64) - 112 + 5 = 128 - 112 + 5 = 21.

The result of g(f(-3)) is 21, which is not listed in the options provided by the student. It seems there is a mistake in the options given. The correct answer should be 21.