Home
Class 12
MATHS
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,x lt x lt 2`
`(x^(2)+1)/(2),2 le x le 3 " " (x^(2)+1)/(3), 3 le x le 3.9`
`f.(x) gt 0` in each of the intervals and so f(x) is increasing in each of the intervals
`:.2 lt f(x) lt 5 "in" 1 le x lt 2, (5)/(2) le f(x) lt "in" 2 le x lt , (10)/(3) le f(x) le (1)/(3) xx 16.21 "in" 3 le x le 3.9`
Hence, the greatest value is `(1)/(3)xx16.21`
Promotional Banner

Similar Questions

Explore conceptually related problems

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

Let f(x) = [x]^(2) + [x+1] - 3 , where [.] denotes the greatest integer function. Then

Let f(x)=(-1)^([x]) where [.] denotes the greatest integer function),then

Let f(x)=sec^(-1)[1+cos^(2)x], where [.] denotes the greatest integer function. Then the

For a function f(x)=(2(x^(2)+1))/([x]) (where [.] denotes the greatest integer function), if 1lexlt4 . Then

Let f(x)=[x]cos ((pi)/([x+2])) where [ ] denotes the greatest integer function. Then, the domain of f is

Let f(x)={1+|x|,x<-1[x],xgeq-1 , where [.] denotes the greatest integer function. The find the value of f{f(-2,3)}dot

If [.] denotes the greatest integer function, then f(x)=[x]+[x+(1)/(2)]

If f(x) = {{:(|1-4x^(2)|",",0 le x lt 1),([x^(2)-2x]",",1 le x lt 2):} , where [] denotes the greatest integer function, then