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Question
A function f: [– 5, 9] → R is defined as follow :
f(x) = `{{:(6x + 1";", -5 ≤ x < 2),(5x^2 - 1";", 2 ≤ x < 6),(3x - 4";", 6 ≤ x ≤ 9):}` Find f(– 3) + f(2)
Solution
f(x) = 6x + 1; x = {– 5, – 4, – 3, – 2, – 1, 0, 1}
f(x) = 5x2 – 1; x = {2, 3, 4, 5}
f(x) = 3x – 4; x = {6, 7, 8, 9}
f(– 3) + f(2)
f(x) = 6x + 1
f(– 3) = 6(– 3) + 1 = – 18 + 1 = – 17
f(x) = 5x2 – 1
f(2) = 5(2)2 – 1 = 20 – 1 = 19
f(– 3) + f(2) = – 17 + 19 = 2
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