1. Tardigrade
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  4. 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

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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

Application of Derivatives

Solution:

$h(x)=f\left(g(x) \quad h^{\prime}(x)=f^{\prime}(g(x)) g^{\prime}(x)<0\right.$
$\therefore h(0)=0 \therefore h(x) \leq 0$
$ \Rightarrow h(x)=0 \forall x \in(0, \infty)$
$\Rightarrow h(x)-h(1)=0$