# is there a function f from the reals to the reals which is not continuous,but has a continous square?

##### 3 Answers

# 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#

Yes, because

#### Explanation:

There's more!

#### Explanation:

In fact, there is a family of functions

Are the required functions. Their square is always