Find the maximum value of f(x)= ( x) for all x R. - Vidyadip

Question

Find the maximum value of $f(x)=\sin (\sin x)$ for all $x \in R$.

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Answer

(c) : We have, $f(x)=\sin (\sin x), x \in R$
Now, $-1 \leq \sin x \leq 1$ for all $x \in R$
$\Rightarrow \sin (-1) \leq \sin (\sin x) \leq \sin 1$ for all $x \in R$
$[\because \sin x$ is an increasing function on $[-1,1]]$
$\Rightarrow \quad-\sin 1 \leq f(x) \leq \sin 1$ for all $x \in R$
This shows that the maximum value of $f(x)$ is $\sin 1$.

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