Let f and g be increasing and decreasing functions respectively from [0, ∞) to [0, ∞). Let h(x)=f(g(x), h(0)=0 then h(x)-h(1) is

Question

Let f and g be increasing and decreasing functions respectively from [0, ∞) to [0, ∞). Let h(x)=f(g(x), h(0)=0 then h(x)-h(1) is (A) always zero (B) always negative (C) always positive (D) increasing

Tardigrade Admin · Accepted Answer

h(x)=f(g(x) h prime(x)=f prime(g(x)) g prime(x)<0. ∴ h(0)=0 ∴ h(x) ≤ 0 ⇒ h(x)=0 ∀ x ∈(0, ∞) ⇒ h(x)-h(1)=0

Q. Let $f$ and $g$ be increasing and decreasing functions respectively from $[0, \infty)$ to $[0, \infty)$ . Let $h (x) = f (g (x), h (0) = 0$ then $h (x) - h (1)$ is

always zero

always negative

always positive

increasing

$h (x) = f (g (x) h^{'} (x) = f^{'} (g (x)) g^{'} (x) < 0$
$∴ h (0) = 0 ∴ h (x) \leq 0$
$\Rightarrow h (x) = 0\forall x \in (0, \infty)$
$\Rightarrow h (x) - h (1) = 0$

Q. Let f and g be increasing and decreasing functions respectively from [0,∞) to [0,∞). Let h(x)=f(g(x),h(0)=0 then h(x)−h(1) is