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Functions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsFunctions1 Mark
Question
Solve the following for $x$, where $|x|$ is modulus function, $[x]$ is the greatest integer function, $\{x\}$ is a fractional part function.

$[x+[x+[x]]]=9$

✓

Answer

$[x+[x+[x]]]=9$
$\therefore[\mathrm{x}+[\mathrm{x}]+[\mathrm{x}]]=9 \ldots \ldots .[\mathrm{x}+\mathrm{n}]=[\mathrm{x}]+\mathrm{n}$, if $\mathrm{n}$ is an integer $]$
$\therefore[\mathrm{x}+2[\mathrm{x}]]=9$
$\therefore[x]+2[x]=9 \ldots .[[2[x]$ is an integer $]]$
$\therefore[\mathrm{x}]=3$
$\therefore \mathrm{x} \in[3,4)$

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