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6

Show that decreases in the interval [0, ∞) and increases in the interval (-∞, 0].

We have,

Case 1

When x [0,)

Let , (0,] and

⇒

⇒

⇒

⇒ f(x_{1})< f(x_{2})

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.