Question

Evaluate (f◦g)(9) without finding an equation for the function. f(x) = −3x−5, g(x) = 9x−9.

A) -162
B) -144
C) -135
D) -144

Answer 1

To evaluate (f∘g)(9), we first find g(9), which is 72, and then apply f to this result, yielding f(72) = -221. The result is not among the provided options, indicating a potential error in the question or the options.

Step-by-step explanation:

The student is asking to evaluate the composite function (f∘g)(9) given f(x) = −3x−5 and g(x) = 9x−9. To do this, we need to follow a two-step process. First, we evaluate g(9) to find the input to the function f. Then we evaluate f using the output of g(9) as the new input.

1. Calculate g(9): g(9) = 9(9) - 9 = 81 - 9 = 72.
2. Calculate f(g(9)): f(72) = -3(72) - 5. This is -216 - 5, which equals -221.

Therefore, (f∘g)(9) equals -221, which is not one of the provided options. There may be an error with the options given to the student or an error in the original functions provided.