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Let f(x)=(x^(2)+2)/([x]),1 le x le3, whe...

Let `f(x)=(x^(2)+2)/([x]),1 le x le3`, where [.] is the greatest integer function. Then the least value of f(x) is

A

2

B

3

C

`3//2`

D

1

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x)={{:(x^(2)+2",",1lexlt2),((x^(2)+2)/(2)",",2lexlt3),((x^(2)+2)/(3),x=3):}`
`therefore" Least value of f(x) in " [1,2]" is "3`
`" Least value of f(x) in "[2,3]" is "3`
`f(3)=(11)/(3)`
`therefore" Least value of f(x) is 3"`
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