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Class 12 Relations And Functions · Mcq Single Correct1 Markstypes_of_functions

Class 12 Maths · Relations And Functions · Mcq Single Correct #3

If \(f:\mathbb{R}\to\mathbb{R}\), \(f(x)=\begin{cases}x|x|-4,&x\in\mathbb{Q}\\x|x|-\sqrt{3},&x\notin\mathbb{Q}\end{cases}\), then \(f(x)\) is

✅ Step-by-Step Solution

Final Answer: Option (D): Many-to-one and into
  1. \(f(2)=f(\sqrt[4]{3})=0\), so the function is many-to-one. The value \(-\sqrt{3}\) is not attained: on the irrational branch it would require \(x=0\); on the rational branch \(x|x|\) is rational and cannot equal \(4-\sqrt{3}\). Thus it is into.

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