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$S_{1} :$ If a function is defined on [a,b] and continuous on (a,b), then it takes its extreme values on [a,b].
$S_{2} :$ Every continuous and bounded function on $(- \infty, \infty)$ takes on its extreme values.

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$S_{1}$ is false and $S_{2}$ is false

$S_{1}$ and $S_{2}$ are true

$S_{1}$ is false and $S_{2}$ is true

$S_{1}$ is true and $S_{2}$ is false

answer is D.

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Detailed Solution

$S_{1} : f (x) = {\begin{cases} 0 i f x = \frac{\pm π}{2}, \frac{π}{2} \\ \tan x i f x \in (\frac{\pm π}{2} \frac{π}{2}) \end{cases} S_{2} : f (x) = \tan^{- 1} x$

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