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The number of solution of the equastion ...

The number of solution of the equastion `|x-1|+|x-2|=[{x}]+{[x]}+1` , where `[.]` and `{.}` denotes greatest integer function and fraction part funstion respectively is :

A

`0`

B

`1`

C

`2`

D

Infinite

Text Solution

Verified by Experts

The correct Answer is:
D
The number of …………..
`AA x epsilon R, {x} epsilon[0,1)`
Hence `[{x}] = 0` ….(i)
Also `AA x epsilon R, [x] epsilon I`
Hence `{[x]} = 0` ….(ii)
Hence the given equation becomes
`|x-1|+|x-2|=1`
`implies x epsilon [1, 2]`
`:.` Number of solutions = infinite
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