Question

Evaluate: f(g(x)) = 4x-5 when gx) = -2x -4.
A. 8x - 21
B. 8x -21
C. 8x - 16

Answer 1

To evaluate f(g(x)), we substitute g(x) into f(x), calculate the result, and find that the correct answer is -8x - 21.

Step-by-step explanation:

The student has asked to evaluate the composition of two functions: f(g(x)) where f(x) = 4x - 5 and g(x) = -2x - 4. To do this, we need to plug the function g(x) into the function f(x).

First, we calculate g(x):
g(x) = -2x - 4.

Next, we substitute g(x) into f(x), so we have:
f(g(x)) = f(-2x - 4) = 4(-2x - 4) - 5.

Now, we distribute the 4 into each term in parentheses:
4 * -2x = -8x and 4 * -4 = -16, thus:
f(g(x)) = -8x - 16 - 5.

Finally, we combine the constant terms:
f(g(x)) = -8x - (16 + 5) = -8x - 21.

Therefore, the correct answer is B. 8x - 21, with a notable correction on the sign which should be negative as computed (-8x - 21).