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(C) The function is defined as $f(x) = 	ext{Min}\{x + 1, |x| + 1\}$.We can analyze this by considering two cases for $x$:Case $1$: $x \ge 0$. Then $|

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$f(x)$ is differentiable everywhere

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(C) The function is defined as $f(x) = 	ext{Min}\{x + 1, |x| + 1\}$.We can analyze this by considering two cases for $x$:Case $1$: $x \ge 0$. Then $|x| = x$,so $f(x) = 	ext{Min}\{x + 1, x + 1\} = x + 1$.Case $2$: $x For $x Thus,$f(x) = x + 1$ for all $x Combining these,$f(x) = x + 1$ for all $x \in R$.Since $f(x) = x + 1$ is a linear polynomial,it is differentiable everywhere in $R$.Therefore,option $C$ is correct.

Let $f:R \to R$ be a function defined by $f(x) = \text{Min}\{x + 1, |x| + 1\}$. Then which of the following is true?

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