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Question
Write the values of f at −3, 5, 2, −1, 0 if
f(x) = `{{:(x^2 + x - 5, "if" x ∈ (−∞, 0)),(x^2 + 3x - 2, "if" x ∈ (3, ∞)),(x^2, "if" x ∈ (0",", 2)),(x^2 - 3, "otherwise"):}`
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Solution
f(x) = `{{:(x^2 + x - 5, "if" x ∈ (−∞, 0)),(x^2 + 3x - 2, "if" x ∈ (3, ∞)),(x^2, "if" x ∈ (0",", 2)),(x^2 - 3, "otherwise"):}`
When x = – 3
f(x) = x2 + x – 5
f(– 3) = (– 3)2 + (– 3) – 5
= 9 – 3 – 5
= 9 – 8
= 1
When x = 5
f(x) = x2 + 3x – 2
f(5) = 52 + 3(5) – 2
= 25 + 15 – 2
= 40 – 2
= 38
When x = 2
f(x) = x2 – 3
f(2) = 22 – 3
= 4 – 3
= 1
When x = – 1
f(x) = x2 + x – 5
f(–1) = (–1)2 – 1 – 5
= 1 – 1 – 5
= – 5
When x = 0
f(x) = x2 – 3
f(0) = 02 – 3
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