1. Tardigrade
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  3. Mathematics
  4. If f:[1,10] arrow[1,10] is a non-decreasing function and g:[1,10] arrow[1,10] is a non-increasing function. Let h(x)=f(g(x)) with h(1)=1, then h(2)

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Q. If $f:[1,10] \rightarrow[1,10]$ is a non-decreasing function and $g:[1,10] \rightarrow[1,10]$ is a non-increasing function. Let $h(x)=f(g(x))$ with $h(1)=1$, then $h(2)$

Application of Derivatives

Solution:

$ x > 1 \Rightarrow f(x) \geq f(1)$
$x > 1 \Rightarrow g(x) \leq g(1) $
$ \Rightarrow f(g(x)) \leq f(g(1)) $
$ \Rightarrow h(x) \leq 1 .....$(i)
Range of $h(x)$ is subset of $[1,10]$
$\Rightarrow h(x) \geq 1.....$(ii)
By (i), (ii) we have $h(x)=1 \Rightarrow h(2)=1$