Home
Class 12
MATHS
If f(x) = 2x and g(x) = (x^(2))/(2)+1 ...

If `f(x) = 2x` and `g(x) = (x^(2))/(2)+1` , then which of the following can be a discontinuous functions?

A

`f(x)+g(x)`

B

`f(x)-g(x)`

C

`f(x).g(x)`

D

`(g(x))/(f(x))`

Text Solution

Verified by Experts

The correct Answer is:
D
We know that, if f and g be continuous functions, then
(a) `f+g` is continuous , (b) `f-g` is continuous
(c ) `fg` is continuous , (d) `(f)/(g)` is continuous at these points, where ` g(x) ne 0`.
Here, ` (g(x))/(f(x)) = ((x^(2))/(2)+1)/(2x)=(x^(2)+2)/(4x)`
Which is discontinuous at `x = 0`.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT EXEMPLAR ENGLISH|Exercise Fillers|10 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT EXEMPLAR ENGLISH|Exercise True/False|10 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT EXEMPLAR ENGLISH|Exercise True/False|10 Videos

  • APPLICATION OF INTEGRALS

    NCERT EXEMPLAR ENGLISH|Exercise Objective Type Questions|22 Videos

  • DETERMINANTS

    NCERT EXEMPLAR ENGLISH|Exercise TRUE/FALSE|11 Videos

Similar Questions

Explore conceptually related problems

If f(x) = (x + 1)/(x-1) and g(x) = (1)/(x-2) , then (fog)(x) is discontinuous at

Let f (x)= signum (x) and g (x) =x (x ^(2) -10x+21), then the number of points of discontinuity of f [g (x)] is

Knowledge Check

  • If f (x) =3 -x and g (x) = (x ^(2))/(2), which of the following is NOT in the range of f (g (x) ?

    A
    `-3`
    B
    0
    C
    2
    D
    4

  • If f(x)=x^(3) and g(x)=x^(2)+1 , which of the following is an odd functionn (are odd functions)? I. f(x)*g(x) II. f(g(x)) III. g(f(x))

    A
    Only I
    B
    only II
    C
    only III
    D
    Only II and III

  • If f(x)=cosx and g(x)=2x+1 , which of the following are even functions? I. f(x)*g(x) II f(g(x)) III. g(f(x))

    A
    only I
    B
    only II
    C
    only III
    D
    Only I and II

    • Similar Questions

    Explore conceptually related problems

    If f(x) = (1)/(x^(2) - 17 x + 66) , then f((2)/(x - 2)) is discontinuous at x =

    If the function f(x)=x^3+e^(x/2) and g(x)=f ^(−1)(x) , then the value of g ′ (1) is

    Suppose f, g, and h be three real valued function defined on R. Let f(x) = 2x + |x|, g(x) = (1)/(3)(2x-|x|) and h(x) = f(g(x)) The domain of definition of the function l (x) = sin^(-1) ( f(x) - g (x) ) is equal to

    If f(x)=(1)/(2)x-4 and f(g(x))=g(f(x)) , which of the following can be g(x) ? I. 2x-(1)/(4) II. 2x+8 III. (1)/(2)x-4

    IF f(x) = sqrt(x) and the composite function f(g(x))= sqrt(4x^2-5) , which of the following could be g(x) ?

    Home
    Profile