Home
Class 12
MATHS
Let f(x) be given that f(x)={{:(,x,"if x...

Let f(x) be given that `f(x)={{:(,x,"if x is rational"),(,1-x,"if x is irrational"):}`
The number of points at which f(x) is continuous, is

A

`oo`

B

1

C

0

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Given, `f(x)={(x",","if "x in Q),(1-x",","if "x in Q^(c)):}`, then f(x) is continuous, if `x=1-x.`
`rArr 2x=1 rArr x=(1)/(2)`
So, f(x) is continuous at `x=(1)/(2).`
i.e. at only one point.
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise EXERCISE 2 (MISCELLANEOUS PROBLEMS)|60 Videos

  • CONTINUITY

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|16 Videos

  • CIRCLE AND CONICS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise All Questions|74 Videos

  • DEFINITE INTEGRALS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|22 Videos

Similar Questions

Explore conceptually related problems

If f(x)={(x",", "if x is rational "),(-x",","if x is irrational"):} , then

If f(x)={{:(1,"x is rational"),(2,"x is irrational"):} then

Let f(x) = [{:(x^(2), " if x is irrational"),(1, " if x is rational"):} , then

Let f defined on [-5, 5] as f(x)={{:("x, if x is rational"),("-x, if x is irrational"):}, then f(x) is

If f (x)= [{:(x,,, "if x is rational"), (1-x,,," if x is irrational "):}, then number of points for x in R, where y =f (f (x)) discontinous is:

f is defined on [-5,5] as f(x)= {{:("x if x is rational"),("-x if x is irrational"):}

Let f (x)= {{:(sin ^(2) x"," , "x is rational"),(-sin ^(2)x",", " x is irrational"):}, then set of points, where f (x) is continuous, is:

If f(x)={x, when x is rational,1-x, when x is irrational,then