Question

Find the points of discontinuity of 

Solution

Correct option is

x = ½,1,2

The function  is discontinuous at the point

                      x = 1.                                                 …(i)

The function  is discontinuous at u = – 2 and u = 1.  

    

   

  

⇒      x – 1 = 1

⇒       x = 2                          … (iii) 

Hence, the composite function y = g(f (x)) is discontinuous at three points

x = 1/2, 1, 2.

SIMILAR QUESTIONS

Q1

Let y = (x) be defined parametrically as y = t2 + t |t|x = 2t – |t|t Ïµ R Then at x = 0, find (x) and discuss continuity.

Q2

 for what value of kf (x) is continuous at x = 0?

Q3

      

Determine a and b such that f (x) is continuous at x = 0.

Q4

 

   

Determine the form of g(x) = f ( f (x)) and hence find the point of discontinuity if g, if any.

Q5

The left hand derivative of f (x) = [x] sin (πx) at x = kk is an integer, is:

Q6

Which of the following functions is differentiable at x = 0?

Q7

Let f (x) = [n + p sin x], x Ïµ (0, π), n Ïµ Z and p is a prime number, where [.] denotes the greatest integer function. Then find the number of points where f (x) is not Differential.

Q8

, then draw the graph of f (x) in the interval [–2, 2] and discuss the continuity and differentiability in [–2, 2]

Q9

Fill in the blank, statement given below let . The set of points where f (x) is twice differentiable is ……………. .

Q10

The function f (x) = (x2 – 1) |x2 – 3x +2| + cos ( | | ) is not differentiable at