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Class 12 Relations And Functions · Mcq Single Correct1 Markstypes_of_functions

Class 12 Maths · Relations And Functions · Mcq Single Correct #30

Let \(f:\mathbb{R}\to\mathbb{R}\) be defined by \(f(x)=\lfloor x\rfloor^2+\lfloor x+1\rfloor-3\). Choose the most complete correct option.

✅ Step-by-Step Solution

Final Answer: Option (D): Both (a) and (b)
  1. Writing \(k=\lfloor x\rfloor\) gives \(f(x)=k^2+k-2=(k+2)(k-1)\). It vanishes on \([-2,-1)\cup[1,2)\). It is constant on unit intervals and has only integer outputs, so on \(\mathbb{R}\to\mathbb{R}\) it is many-one and into.

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