It is said that g(x)=x^2=f(x)timesf(x) is a continuous function.But i have a doubt that its not continuous as 2^2=4,3^2=9.....but there is discontinuity in numbers like 2,3,5,7...please elaborate.

Asked by Anagha Plus two | 26th Jul, 2011, 03:37: AM

Expert Answer:

In simple words,we can say a function is continous if we can draw the graph of the function without lifting the pencil from our paper.
Now,in your question ,both functions f(x) and g(x),defined as g(x)=x2=[f(x)]2
are continous everywhere being polynomial functions.Even ,as a check you can draw their graphs,which come out to be continous curves.
g(x)=x2 is a parabola and f(x)=±x are straight lines passing through origin.
The formal defination of continuity also holds here for any 'c'in the domain of the functions:
i.e both f(x) and g(x) are well defined at 'c' and the value of the function at x= c equals the limit of the functions at 'c'.
Thus,there are no points of discontinuity of f or g.

Answered by  | 26th Jul, 2011, 10:17: AM

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