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

# Determine The Form Of g(x) = f ( f (x)) And Hence Find The Point Of Discontinuity If g, If Any.

#### Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

#### Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

#### National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

#### Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

#### Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

## Question

### Solution

Correct option is

x Ïµ [0, 1]  (1, 2)

Hence,

Now, if (1 + x) Ïµ [1, 2] then

f (1 – x) = 1 + (1 + x) = 2 + x             … (i)

[from original definition of f (x)]

Similarly, if (1 + x) Ïµ (2, 3) then

f (1 + x) = 3 – (1+ x) = 2 – x               … (ii)

If (3 – x) ≤ (0, 1)

f (3 – x) = 1 + (3 – x) = 4 – x             … (iii)

Using (i), (ii) and (iii), we get

Here, as g(x) changes the inequality sign at x = 1 and x = 2.

Thus, to check continuity at x = 1 and x = 2.

Now we will check the continuity of g(x) at x = 1, 2

At x = 1

As LHL ≠ RHL, g(x) is discontinuous at x = 1.

At x = 2

As. LHL ≠ RHL, g(x) is discontinuous at x = 2.

Thus, g(x) is continuous for all x Ïµ [0, 1] ∪ (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

Find the points of discontinuity of

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