For $\mathrm{f}(x)=[x]$, whe inction. which of the following is tru very $x \in \mathbb{R}$
For $\mathrm{f}(x)=[x]$, whe inction. which of the following is tru very $x \in \mathbb{R}$
[x]+1=x
$[x]+1 \leq x$
$[x]+1>x$
$[x]+1 < x$
Solution
$[\mathrm{x}]$ 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 $0 < x-[x] < 1$
$\therefore x < [x]+1$