Question

Let f and g be increasing and decreasing functions respectively from [0, ∞) to [0, ∞). Let h (x) = f(g(x)). If h (0) = 0, then h(x) is

(a) Always zero

(b) Always negative

(c) Always positive

(d) Strictly increasing

Answer 1

Correct option (a) Always zero

Explanation:

Since g(x) is decreasing,

∴ g (x2 ) ≤ g (x1 ) when x2 ≥ x1 .

Since f(x) is increasing,

∴ f [g(x1 )] ≥ f [g(x2)]

⇒h(x1) ≥ h(x2) when x2 ≥ x1 .

⇒ h(x) is a decreasing function of x and h(0) = 0.

Also, domain of h = [0, ∞) and range of h = [0, ∞).