HCU MCA 2013 Paper

Question : 27 of 75

Marks: +1, -0

Use the notation |x| to denote the absolute value of x, and |x I denotes the largest integer smaller or equal to x. For a, an integer, such that a > 1 let f(x) be given by
f(x) =

\{\table {||\x-1|-1|,}, \x<\a ; {|\x|,}, \x≥\a

Which of the following is the set of points of discontinuity for the function f(x)?

All integers ≥ - a
All integers ≥ a
All integers > a
a

Validate

Solution:

\{\table {||\x-1|-1|,}, \x<\a ; {|\x|,}, \x≥\a

, where a > 1

\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=\{\table {1-\x-1|,}, \x<\a ; {[\x],}, \x≥\a

\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=\{\table {\x,}, \x<\a ; {[\x],}, \x≥\a

Hence, f(x) is discontinuous all integer> a.

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