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Let f(x)=(x^(2)+1)/([x]),1 lt x le 3.9.[...

Let `f(x)=(x^(2)+1)/([x]),1 lt x le 3.9.[.]` denotes the greatest integer function. Then

A

f (x) is increasing function

B

f (x) is decreasing function

C

The greatest value of f (x) is `(1)/(3)xx16.21`

D

The least value of f (x) is 2

Text Solution

Verified by Experts

The correct Answer is:
C
Here, `f(x)=x^(2)+1, 1 lt x lt 2`
`(x^(2)+1)/(2), 2le xlt 3," "(x^(2)+1)/(3), 3le x le3.9`
`f'(x) gt0` in each of the intervales and so `f(x)` is increasing in each of the intervals
`therefore" "2 ltf(x) lt 5" in "1 lt x lt2,(5)/(2) le f(x) lt 5" in "2le xlt 3,(10)/(3) le f(x) le (1)/(3) xx16.21" in " 3le x le 3.9`
Hence, the greatest value is `(1)/(3)xx16.21`
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