Show that is neither increasing nor decreasing on R.

Question

Philoid · Accepted Answer

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.