Tessellate S.T.E.M.S - Mathematics - College - Set 2 - Problem 3

Let $f$ be a function $f(x) = \left|\sin \left(\frac{1}{x}\right)\right|$ for $x \neq 0, f(0) = 0$ .

$\textbf{Statement 1}$ . For any continous function $g : \mathbb{R} \rightarrow \mathbb{R}$ , $f+g$ follows the intermediate value property .

$\textbf{Statement 2}$ . For any function $g : \mathbb{R} \rightarrow \mathbb{R}$ following the intermediate value property, $f+g$ follows the intermediate value property.

Which of the above statements is correct?

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This problem is a part of Tessellate S.T.E.M.S.