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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.