Engineering
Mathematics
Introduction to Functions
Question
If f : R → R, f(x) = tan–1 x + (a2 – 3a + 2) ln (|x| + 1) + (a – 3)(b + 2) e–x is a bounded function, then find the number of ordered pairs (a, b) .
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Solution
For f (x) to be bounded
a2 – 3a + 2 = 0 ⇒ a = 1, 2, and b + 2 = 0 ⇒ b = –2
Number of ordered pairs (a, b) are 2.