Let f:(1,3) to R be a function defined ...

Let `f:(1,3) to R` be a function defined by `f(x)=(x[x])/(1+x)` , where [x] denotes the greatest integer `le x` . Then the range of f is :

A

`(1/2,3/2)`

B

`(1/2,1)uu[4/3,oo)`

C

`(1/2,2/3)uu[4/3,3/2)`

D

`(1,4/3)`

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The correct Answer is:

C

`f(x) ={{:(x/(1+x),,,x in (1,2)),((2x)/(x+1),,,x in[2,3)):}`
is increasing function `:." "f(x) in (1/2 2/3 )uu[4/3,3/2)`

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