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Show that the function f (x) = x2 is strictly increasing function on [0,∞).
Asked by Topperlearning User | 06 Aug, 2014, 08:12: AM

Let x1, x2 [0,¥) such that x1 < x2. Then,

x1 < x2  => x12x1x2..........(i) [Multiplying both sides by x1]

and, x1 < x2  => x1x2<x22 ............ (ii) [Multiplying both sides by x2]

From (i) and (ii), we get

x1 < x2 => x12 < x22 => f (x1) < f (x2)

Thus, x1 < x2 => f (x1) < f (x2) for all x1, x2­  [0, ¥)

Hence, f (x) is strictly increasing function on [0, ¥)

Answered by | 06 Aug, 2014, 10:12: AM

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