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Discuss the continuity of function 
  • a)
    discontinuous at x=1
  • b)
    discontinuous at x=±1
  • c)
    continuous everywhere.
  • d)
    discontinuous at x=-1
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Discuss the continuity of function a)discontinuous at x=1b)discontinuo...
f(x) = |x-1| + |x+1| , x € R

► For x ≥ 1,
f(x) = x-1 + x+1
f(x) = 2x

► For -1 ≤ x ≤ 1,
f(x) = -x + 1 + x+1
f(x) = 2

► For x ≤ -1,
f(x) = -x + 1 - x-1
f(x) = -2x


As the graph of f(x) shows, the function is continuous throughout its domain.
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Discuss the continuity of function a)discontinuous at x=1b)discontinuo...
Dear, the rough graph of given equation look like this, which you can make comfortably as I consider. From, this graph, you can easily tell this that it is continuous everywhere.. One more thing for you from my side is this that Modulus functions are always continuous..
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