MHT CET · Maths · Functions
For \(\mathrm{f}(x)=[x]\), whe inction. which of the following is tru very \(x \in \mathbb{R}\)
- A [x]+1=x
- B \([x]+1 \leq x\)
- C \([x]+1>x\)
- D \([x]+1 < x\)
Answer & Solution
Correct Answer
(D) \([x]+1 < x\)
Step-by-step Solution
Detailed explanation
(B)
\([\mathrm{x}]\) is the greatest integer function. This means, the greatest integer is less than or equal to \(\mathrm{x}\).
If \(\mathrm{x}\) is an integer, then \([\mathrm{x}]=\mathrm{x}\).
If \(x\) is a non integer number, then \([x] < x\) and \(0 < x-[x] < 1\)
\(\therefore x < [x]+1\)
\([\mathrm{x}]\) is the greatest integer function. This means, the greatest integer is less than or equal to \(\mathrm{x}\).
If \(\mathrm{x}\) is an integer, then \([\mathrm{x}]=\mathrm{x}\).
If \(x\) is a non integer number, then \([x] < x\) and \(0 < x-[x] < 1\)
\(\therefore x < [x]+1\)
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