Solve Continuous Functions Equation: (f(x)^2)= x^2

[Justabeginner]

Homework Statement

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

Homework Equations

The Attempt at a Solution

What method should I use to solve this? Is there a specific strategy involved besides plug and chug? Off the top of my head, I can only think of f(x)= x, but that's just one. Thank you.

 

[Office_Shredder]

If you take square roots:
$$\sqrt{ a^2} = |a|$$
Is always a true statement regardless of whether a is positive or negative. So for your equation you get |f(x)| = |x|. Try working from there

 

[Justabeginner]

Thank you so much for that derivation!
For this absolute function, there would be two possible values: -x and x.
There would only be two functions possible then I think?
I thought it would be more complicated, and involve log functions, etc.