Question

4. Find (fºg)(x) where f(x) = 3x + 1, g(x) = 2x + 7.

A. (f•g)(x) = 5x + 8
B. (f•g)(x) = 6x2 + 13x + 7
C. (f•g)(x) = 6x2 + 23% + 7
D.(f.g)(x) = 6x² + 7

Answer 1

The composition (f°g)(x) of the functions f(x) = 3x + 1 and g(x) = 2x + 7 is calculated as 6x + 22, suggesting there is a typo in the provided answer choices.

Step-by-step explanation:

To find (f\u00b0g)(x), which is also known as the composition of the functions f(x) and g(x), we substitute g(x) into f(x). Given f(x) = 3x + 1 and g(x) = 2x + 7, we compute f(g(x)).

We start by calculating g(x):
g(x) = 2x + 7.

Then we substitute g(x) into f(x):
f(g(x)) = f(2x + 7) = 3(2x + 7) + 1.

Now, we simplify this expression:
f(g(x)) = 3(2x) + 3(7) + 1 = 6x + 21 + 1 = 6x + 22.

Therefore, the composition (f\u00b0g)(x) is 6x + 22, which does not match any of the options provided in the question. There appears to be a typo in the options or the question might be incomplete. Nonetheless, the correct composition of f(x) and g(x) is 6x + 22.