Question

Given f(x)=9x^2 and g(x)= root 12− 3/x, find (f∘g)(−4).
a) 36
b) −36
c) 48
d)−48

Answer 1

To find (f ∘ g)(-4), we evaluate g(-4) first and then apply f(x) to that result, yielding a value that does not match any of the provided options. There seems to be a mistake either in the problem statement or the answer choices, as the correct result is not listed.

Step-by-step explanation:

The student has asked to find (f ∘ g)(-4), where f(x) = 9x2 and g(x) = √(12 - 3/x). To find (f ∘ g)(x), you first apply g(x) and then apply f(x) to the result. Let's do this step-by-step for x = -4:

1. First, evaluate g(-4): g(-4) = √(12 - 3/(-4)) = √(12 + 3/4) = √(12 + 0.75) = √(12.75).
2. Then, square the result of g(-4) to apply f(x): f(g(-4)) = 9 * (12.75)2.
3. Finally, calculate the square of 12.75, which gives 162.5625. Multiplying by 9, we obtain 1463.0625, which is not an option in the given choices. Therefore, there may be a mistake in the student's question or the options provided.

None of the answer options (a) 36, (b) -36, (c) 48, (d) -48 match with the calculated result.