Is there a way to find out axes of symmetry for specific range of function (or check if given line is axis of symmetry)?

Question

my first post here. Sorry if my language won't be clear or professional.

I'm wondering if it is possible to check for example if function $ f(x)=x^{2} ~$ has axis of symmetry for $x ~\epsilon <0,1> $. My first guess was $~y=-x+1~$, is there a way to check it? Or achieve this kind of equation through some mathematical procedure?

I know it is not axis of symmetry, but I wonder if there is simple way of checking it.

Thanks in advance.

Answer 1

HINT:

$f(x)$ has a line of symmetry at $x= a$ if

$f(x) = f(a-x)$