Question

How many continuous functions f are there which satisfy (f(x))^2 = x^2 for all x?

Answer 1

\[\sqrt{*}\] is continuous, so |f(x)| = |x|. f(x) = x, or f(x) = -x or f(x) = |x| or f(x) = -|x|.

Answer 2

hmmm looks okay

Answer 3

I didn't use those book)

Answer 4

i see