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Question
Let f: R → R be defined by f(x) = `{{:(2x",", x > 3),(x^2",", 1 < x ≤ 3),(3x",", x ≤ 1):}`. Then f(–1) + f(2) + f(4) is ______.
Options
9
14
5
None of these
Solution
Let f: R → R be defined by f(x) = `{{:(2x",", x > 3),(x^2",", 1 < x ≤ 3),(3x",", x ≤ 1):}`. Then f(–1) + f(2) + f(4) is 9.
Explanation:
Given that, f(x) = `{{:(2x",", x > 3),(x^2",", 1 < x ≤ 3),(3x",", x ≤ 1):}`
f(–1) = 3(–1) = –3 .....(Using f(x) = 3x)
f(2)= 22 = 4 ......(Using f(x) = x2)
f(4) = 2(4) = 8 ......(Using f(x) = 2x)
∴ f(–1) + f(2) + f(4) = 3 + 4 + 8 = 9
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