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Q.
Which of the following best represents the graph of $f(x)=\tan (\sin x), x \geq 0$ ?
Application of Derivatives
Solution:
$f ( x )=\tan (\sin x)$ is an odd function on $(-\infty, \infty)$.
Range of $f(x)=[-\tan 1, \tan 1]$.
Also, $f(x)$ is continuous and differentiable for all $x \in R$
Note that, $\tan 1>1$ and $-\tan 1<-1$.
Also, $f ( x )$ is periodic with fundamental period $2 \pi$.