Question

Given f(x) = |x| and g(x) = 20/x² + 4, find the following expressions.

(a) (f∘g)(4) =
(b) (g∘f)(2) =
(c) (f∘f)(1) =
(d) (g∘g)(0) =

Answer 1

Composite functions (f∘g)(4), (g∘f)(2), and (f∘f)(1) have been calculated with the values 5.25, 9, and 1 respectively, while (g∘g)(0) is undefined due to the division by zero.

Step-by-step explanation:

The question relates to evaluating composite functions. Here's a step-by-step guide to finding the specified composite function values:

1. (f∘g)(4): First calculate g(4), then apply f to the result. g(4) = 20/4² + 4 = 20/16 + 4 = 1.25 + 4 = 5.25. Then, f(5.25) = |5.25|, which is 5.25.
2. (g∘f)(2): First calculate f(2), then apply g to that result. f(2) is |2|, which is 2. Then, g(2) = 20/2² + 4 = 20/4 + 4 = 5 + 4, which equals 9.
3. (f∘f)(1): First calculate f(1), then apply f again to that result. f(1) is |1|, which is 1. Then, f(1) is again |1|, which remains 1.
4. For (g∘g)(0), g(0) would involve division by zero, which is undefined, so (g∘g)(0) is undefined as well.

Therefore, our answers to the student's questions are: (a) (f∘g)(4) = 5.25 (b) (g∘f)(2) = 9 (c) (f∘f)(1) = 1 (d) (g∘g)(0) is undefined.