Question 1145907
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Consider this function, defined on the number line for all real numbers

              / 0 if x is irrational,
             |  
    f(x) =  <
             | 
              \ 1 if x is rational.


This function is discontinued at every point on the number line.


Next consider function  g(x) = 1 - f(x).


This function is discontinued at every point on the number line, too.


But the sum of these two functions  f(x) +g(x) = f(x) + (1 - f(x)) == 1  is identically equal to 1 
in all number line and is, therefore, continue function in all points of the number line.
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