Show that is neither increasing nor decreasing on R.

We have,


Case 1


When x [0,)


Let >





f(x1) < f(x2)


f(x) is decreasing on[0,∞).


Case 2


When x (-,0]


Let >






f(x) is increasing on(-∞,0].


Thus, f(x) is neither increasing nor decreasing on R.


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