Let f(x) = 2x + 1 and g(x) = x^2. Compute (f∘g)(-2) and (g∘f)(-2).

Let f(x) = 2x + 1 and g(x) = x^2. Compute (f∘g)(-2) and (g∘f)(-2).

• A. (f∘g)(-2) = 9; (g∘f)(-2) = 9
• B. (f∘g)(-2) = 9; (g∘f)(-2) = 4
• C. (f∘g)(-2) = 4; (g∘f)(-2) = 9
• D. (f∘g)(-2) = 4; (g∘f)(-2) = 4

Answer: (A)

Composition means you apply the inner function first, then the outer one. For the first composition at -2: find g(-2) = (-2)² = 4, then f(4) = 2·4 + 1 = 9. So (f∘g)(-2) = 9. For the second composition at -2: find f(-2) = 2(-2) + 1 = -3, then g(-3) = (-3)² = 9. So (g∘f)(-2) = 9. Both expressions evaluate to 9, so the results are 9 and 9.

Composition means you apply the inner function first, then the outer one.

For the first composition at -2: find g(-2) = (-2)² = 4, then f(4) = 2·4 + 1 = 9. So (f∘g)(-2) = 9.

For the second composition at -2: find f(-2) = 2(-2) + 1 = -3, then g(-3) = (-3)² = 9. So (g∘f)(-2) = 9.

Both expressions evaluate to 9, so the results are 9 and 9.