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Question
Write the values of f at − 4, 1, −2, 7, 0 if
f(x) = `{{:(- x + 4, "if" - ∞ < x ≤ - 3),(x + 4, "if" - 3 < x < -2),(x^2 - x, "if" - 2 ≤ x < 1),(x - x^2, "if" 1 ≤ x < 7),(0, "otherwise"):}`
Solution
f(x) = `{{:(- x + 4, "if" - ∞ < x ≤ - 3),(x + 4, "if" - 3 < x < -2),(x^2 - x, "if" - 2 ≤ x < 1),(x - x^2, "if" 1 ≤ x < 7),(0, "otherwise"):}`
When x = − 4
f(x) = – x + 4
f(−4) = – (− 4) + 4
= 4 + 4
= 8
When x = 1
f(x) = x – x2
f(1) = 1 – 12
= 1 – 1
= 0
When x = −2
f(x) = x2 – x
f(−2) = (−2)2 – (−2)
= 4 + 2
= 6
When x – 7
f(x) = 0
⇒ f(7) = 0
When x = 0
f(x) = x2 – x
⇒ f(0) = 02 – 0
= 0
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