Home
Class 12
MATHS
Two mappings f:R to R and g:R to R are d...

Two mappings `f:R to R` and `g:R to R` are defined as follows:
`f(x)={(0,"when x is rational"),(1,"when x is irrational"):}` and
`g(x)={(-1,"wnen x is rational"),(0,"when x is irrational"):}` then the value of `[(gof)(e)+(fog)(pi)]` is -

A

0

B

-1

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
B
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • MCQ ZONE

    CHHAYA PUBLICATION|Exercise Question Paper 7|80 Videos

  • MCQ ZONE

    CHHAYA PUBLICATION|Exercise Question Paper 8|80 Videos

  • MAXIMA AND MINIMA

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination E|2 Videos

  • MCQ ZONE 3

    CHHAYA PUBLICATION|Exercise Question Paper 8|30 Videos

Similar Questions

Explore conceptually related problems

If f(x)={{:("2x+3, when x is an rational ,"),(x^(2)+1", when x is irrational,"):} then f(0) =

If f(x) = 2x + 3, then x is rational. =x^(2)+1 , when x is irrational. then find - (a) f(0), (b) f(pi) .

Knowledge Check

  • A function is defined as, f(x)={(0, where x is rational),(1, where x is irrational)}: . Then f(x) is

    A
    continuous for all `x in R`
    B
    continuous for all `x in R-{0}`
    C
    continuous for all `x in R-{0,1}`
    D
    discontinuous for all `x in R`

  • Let f:RrarrR be defined as . f(x)={(0, "x is irrational"),(sin|x|,"x is irrational"):} Then which of the following is true?

    A
    f is discontinuous for all x
    B
    f is continuous for all x
    C
    f is discontinuous at `x=kpi`, where kis an integer
    D
    f is continuous at `x=kpi`, where kis an integer

  • Let f(x)={(-1+sinK_1pix, x is rational), (1+cosK_2pix, x is irrational) :} If f(x) is periodic function, then:

    A
    either `K_1, K_2in rational or K_1, K_2 in irrational`
    B
    `K_1, K_2 in` rational only
    C
    `K_1 and K_2 in ` irrational only
    D
    `K_1 and K_2 in` irrational such `K_1/K_2` is rational.

    • Similar Questions

    Explore conceptually related problems

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

    Let f: R to R be defined as f(x)={{:(0", x is irrational"),(sin|x|", x is rational"):} Then which of the following is true?

    IF f(x)={{:(x,"if",x,"is rational"),(1-x,"if",x, "is irrational"):},"then find" lim_(xto1//2) f(x) if exists.

    Discuss the continuity of the following function : f(x)={1,if x is rational , 0 ,if x is irrational

    Let f:R to R and g:R to R is define by f(x)=2x+3 and g(x)=3x-2 , then find (f circ g)(-1)

    Home
    Profile