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Question

The function fx=x1+x is
(a) strictly increasing
(b) strictly decreasing
(c) neither increasing nor decreasing
(d) none of these

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Solution

(a) strictly increasing

fx=x1+xCase 1: When x>0, x=xfx=x1+x =x1+xf'x=1+x1-x11+x2 =11+x2>0, xRSo, fx is strictly increasing when x > 0.Case 2: When x<0, x=-xfx=x1+x =x1-xf'x=1-x1-x-11-x2 =11-x2>0, xRSo, fx is strictly increasing when x < 0.Thus, fx is strictly increasing on R.

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