is there a function f from the reals to the reals which is not continuous,but has a continous square?
3 Answers
Apr 17, 2017
f(x) = { (-1, x lt 0), (1, x ge 0) :}
Explanation:
Consider the following function
f(x) = { (-1, x lt 0), (1, x ge 0) :}
This has a discontinuity when
However
f^2(x) = { ((-1)^2, x lt 0), (1^2, x ge 0) :} = 1
Apr 17, 2017
Yes, because
Explanation:
Apr 17, 2017
There's more!
Explanation:
In fact, there is a family of functions
Are the required functions. Their square is always