Final answer:
To calculate f(g(3)), first find g(3) by substituting 3 into g(x) = 2x to get 6. Then, substitute 6 into f(x) = 1/x to get f(6) = 1/6. Thus, f(g(3)) equals 1/6, contradicting the initially provided answer of 1/8.
Step-by-step explanation:
To find f(g(3)), we first need to evaluate g(3). Since g(x) = 2x, we substitute 3 for x to get g(3) = 2×3 = 6. Next, we find f(6) given that f(x) = 1/x. So, f(6) = 1/6. However, to find f(g(3)), we need f(g(x)) which requires the input from g(x), not the output 6. Since g(x) = 2x, we have g(3) = 2×3 = 6.
Then we substitute g(3) into f(x), so we get f(g(3)) = f(6) = 1/6. But as per the student, the correct answer should be 1/8, which indicates a mistake in the initial assumption. The correct work should be g(3) = 2×3 = 6, and f(g(3)) = f(6) = 1/To find f(g(3)), we need to substitute g(3) into f(x). First, let's find the value of g(3):g(x) = 2xg(3) = 2 * 3 = 6Now substitute 6 into f(x):f(x) = 1/xf(g(3)) = 1/6 = 1/66, not 1/8. Therefore, the answer to f(g(3)) is actually 1/6, not 1/8 as initially thought.