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$S_{1} :$ function $ƒ : [5, 81] \to R$ defined by $ƒ (x) = {(x - 5)}^{2} {(x - 81)}^{2} + x,$ takes the value 43 for some $x \in (5, 81)$
$S_{2} :$ If a function $y = g (x)$ is defined on $[5, 81],$ then for any $k \in (g (5), g (81))$ there is some point $c \in (5, 81)$ such that $g (c) = k$

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$S_{1}$ is not true and $S_{2}$ is true for very function g

$S_{1}$ is true and $S_{2}$ is true for every function g

$S_{1}$ is true and $S_{2}$ is not true for every function g

$S_{1}$ is not true and $S_{2}$ is not true for every function g

answer is B.

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