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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) cup [(4)/(3),infty)`

C

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

D

`(1,(4)/(3)]`

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x) ={{:(x/(1+x), , ,x in (1,2)),((2x)/(x+1), ,, x in [1,3)):}`
`f(x)` is increasing function `therefore f(x) in (1/2 ,2/3) uu [4/3 ,3/2)`
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