Mathematics Exam  >  Mathematics Questions  >  Let l = { 1 } ∪ { 2 } For x ∈ R, let... Start Learning for Free
Let l  = { 1 } ∪ { 2 }  For x ∈ R, let φ(x) = dis (x, l) = ln f{| x —y | : y ∈ l} then
  • a)
    φ is discontinuous some where or R
  • b)
    φ is continuous on R but not differentiable only at x = 1
  • c)
    φ is continuous on R but not differentiable only at x = 1 and 2
  • d)
    φ is continuous on R but not differentiable only at 
    x = 1, 3/2 and 2 
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Let l = { 1 } ∪ { 2 } For x ∈ R, letφ(x) = dis (x, l) = l...
Given that,

= ln f{|x -.y| : y ∈ 1}
where l = { l } ∪ { 2 }
= ln f{| x -l| ,| x -2 | } 
the graph of the φ(x) is given by.

Clearly, the graph of the function have sharp edges at x = 1,3/2 and 2. Therefore, f(x) is not differentiable at x
= 1, 3/2 and 2.
Hence, φ(x) is continuous on R but not
differentiable at x = 1, 3/2 and 2
View all questions of this test
Most Upvoted Answer
Let l = { 1 } ∪ { 2 } For x ∈ R, letφ(x) = dis (x, l) = l...
Given that,

= ln f{|x -.y| : y ∈ 1}
where l = { l } ∪ { 2 }
= ln f{| x -l| ,| x -2 | } 
the graph of the φ(x) is given by.

Clearly, the graph of the function have sharp edges at x = 1,3/2 and 2. Therefore, f(x) is not differentiable at x
= 1, 3/2 and 2.
Hence, φ(x) is continuous on R but not
differentiable at x = 1, 3/2 and 2
Free Test
Community Answer
Let l = { 1 } ∪ { 2 } For x ∈ R, letφ(x) = dis (x, l) = l...
Given that,

= ln f{|x -.y| : y ∈ 1}
where l = { l } ∪ { 2 }
= ln f{| x -l| ,| x -2 | } 
the graph of the φ(x) is given by.

Clearly, the graph of the function have sharp edges at x = 1,3/2 and 2. Therefore, f(x) is not differentiable at x
= 1, 3/2 and 2.
Hence, φ(x) is continuous on R but not
differentiable at x = 1, 3/2 and 2
Explore Courses for Mathematics exam
Let l = { 1 } ∪ { 2 } For x ∈ R, letφ(x) = dis (x, l) = ln f{| x —y | : y ∈l} thena)φ is discontinuous some where or Rb)φ is continuous on R but not differentiable only at x = 1c)φ is continuous on R but not differentiable only at x = 1 and 2d)φ is continuous on R but not differentiable only atx = 1, 3/2 and 2Correct answer is option 'D'. Can you explain this answer?
Question Description
Let l = { 1 } ∪ { 2 } For x ∈ R, letφ(x) = dis (x, l) = ln f{| x —y | : y ∈l} thena)φ is discontinuous some where or Rb)φ is continuous on R but not differentiable only at x = 1c)φ is continuous on R but not differentiable only at x = 1 and 2d)φ is continuous on R but not differentiable only atx = 1, 3/2 and 2Correct answer is option 'D'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let l = { 1 } ∪ { 2 } For x ∈ R, letφ(x) = dis (x, l) = ln f{| x —y | : y ∈l} thena)φ is discontinuous some where or Rb)φ is continuous on R but not differentiable only at x = 1c)φ is continuous on R but not differentiable only at x = 1 and 2d)φ is continuous on R but not differentiable only atx = 1, 3/2 and 2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let l = { 1 } ∪ { 2 } For x ∈ R, letφ(x) = dis (x, l) = ln f{| x —y | : y ∈l} thena)φ is discontinuous some where or Rb)φ is continuous on R but not differentiable only at x = 1c)φ is continuous on R but not differentiable only at x = 1 and 2d)φ is continuous on R but not differentiable only atx = 1, 3/2 and 2Correct answer is option 'D'. Can you explain this answer?.
Solutions for Let l = { 1 } ∪ { 2 } For x ∈ R, letφ(x) = dis (x, l) = ln f{| x —y | : y ∈l} thena)φ is discontinuous some where or Rb)φ is continuous on R but not differentiable only at x = 1c)φ is continuous on R but not differentiable only at x = 1 and 2d)φ is continuous on R but not differentiable only atx = 1, 3/2 and 2Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics. Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.
Here you can find the meaning of Let l = { 1 } ∪ { 2 } For x ∈ R, letφ(x) = dis (x, l) = ln f{| x —y | : y ∈l} thena)φ is discontinuous some where or Rb)φ is continuous on R but not differentiable only at x = 1c)φ is continuous on R but not differentiable only at x = 1 and 2d)φ is continuous on R but not differentiable only atx = 1, 3/2 and 2Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Let l = { 1 } ∪ { 2 } For x ∈ R, letφ(x) = dis (x, l) = ln f{| x —y | : y ∈l} thena)φ is discontinuous some where or Rb)φ is continuous on R but not differentiable only at x = 1c)φ is continuous on R but not differentiable only at x = 1 and 2d)φ is continuous on R but not differentiable only atx = 1, 3/2 and 2Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Let l = { 1 } ∪ { 2 } For x ∈ R, letφ(x) = dis (x, l) = ln f{| x —y | : y ∈l} thena)φ is discontinuous some where or Rb)φ is continuous on R but not differentiable only at x = 1c)φ is continuous on R but not differentiable only at x = 1 and 2d)φ is continuous on R but not differentiable only atx = 1, 3/2 and 2Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Let l = { 1 } ∪ { 2 } For x ∈ R, letφ(x) = dis (x, l) = ln f{| x —y | : y ∈l} thena)φ is discontinuous some where or Rb)φ is continuous on R but not differentiable only at x = 1c)φ is continuous on R but not differentiable only at x = 1 and 2d)φ is continuous on R but not differentiable only atx = 1, 3/2 and 2Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Let l = { 1 } ∪ { 2 } For x ∈ R, letφ(x) = dis (x, l) = ln f{| x —y | : y ∈l} thena)φ is discontinuous some where or Rb)φ is continuous on R but not differentiable only at x = 1c)φ is continuous on R but not differentiable only at x = 1 and 2d)φ is continuous on R but not differentiable only atx = 1, 3/2 and 2Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Mathematics tests.
Explore Courses for Mathematics exam
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev