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Question
\[f : R \to R \text{given by} f\left( x \right) = x + \sqrt{x^2} \text{ is }\]
Options
injective
surjective
bijective
None of these
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Solution
\[f\left( x \right) = x + \sqrt{x^2} = x \pm x = 0\text{ or 2x}\]
\[\Rightarrow \text{Each element of the domain has 2 images}.\] ⇒ f is not a function.
So, the answer is (d).
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