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Given f(x) = 3x + 4, g(x) = x² + 1 for x >= 1 and 2x + 3 for x < 1, and h(x) = e^x for x >= 5, 2x² + 3x for 2 <= x < 5, and 5 - x for x < 2. Evaluate h(f(g(-2))).

1. 4
2. 1
3. e⁷
4. 13

Correct answer: 4

Solution

g(-2): since -2 < 1, g = 2(-2)+3 = -1. f(-1) = 3(-1)+4 = 1. h(1): since 1 < 2, use the branch 5 - x = 5 - 1 = 4. Therefore h(f(g(-2))) = 4.

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