Home
Class 12
MATHS
Let f(x)=[x^(2)+1],([x] is the greatest ...

Let `f(x)=[x^(2)+1],([x]` is the greatest integer less than or equal to x)`. Ther

A

on `[1,3]`

B

for all x in `[1,3]` except four points

C

for all x in `[1,3]` except saven points

D

for all x in `[1,3]` except eight points

Text Solution

Verified by Experts

The correct Answer is:
D
f is discontinuous at x for which `x^(2)+1 in I`. For `x in (1, 3)` we have `x^(2) +1 in (2, 10)` so there are seven values. f is clearly continuous from right at 1 but discontinuous from left at 3.
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f(x)=[2x^3-6] , where [x] is the greatest integer less than or equal to x. Then the number of points in (1,2) where f is discontinuous is

Let f(x)=(x)/(1+x^(2)) and g(x)=(e^(-x))/(1+[x]) where [x] is the greatest integer less than or equal to x. Then

If f(x)=|x-1|-[x] , where [x] is the greatest integer less than or equal to x, then

Find all the points of discontinuity of the greatest integer function defined by f(x)=[x], where [x] denotes the greatest integer less than or equal to x.

Let f (x) = [x], where [x] denotes the greatest integer less than or equal to x . If a = sqrt(2011^(2) + 2012) , then the value of f (x) is equal to

Let f:R rarr R be a function defined by f(x)={[[x],x 2 where [x] is the greatest integer less than or equal to x. If I=int_(-1)^(2)(xf(x^(2)))/(2+f(x+1))dx, then the value of (4I-1) is

If f: R to R, defined as f(x)=(sin([x]pi))/(x^(2)+x+1) , where (x] is the greatest integer less than or equal to x, then

Let f(x) be defined by f(x)=x-[x],0!=x in R, where [x] is the greatest integer less than or equal to x then the number of solutions of f(x)+f((1)/(x))=1

If f(x)=|x-1|-[x] (where [x] is greatest integer less than or equal to x ) then.

let f:R rarr R be given by f(x)=[x]^(2)+[x+1]-3, where [x] denotes the greatest integer less than or equal to x. Then,f(x) is