function and inverse symmetry

[J.branco]

i'm trying to prove that a funtion f(being f injective, and it's inverse are symmetric to the line y=x

 

i can prove that the any segment defined by the points (fx,x) (x,fx) is perpendicular to that line, which also contains the midpoint of the segment.

SO the line is the perpendicular bisector to any segment (fx,x)(x,fx)

 

however i realy don't know where to go next? is this enough?whats is the definition of symmetry axe?

[EvoN1020v]

Are you talking about the axis of symmetry? If so, it's the line middle of a parabola.

 

e.g. [math]x^{2}-4x+2[/math]

 

Axis of symmetry is [math]x=2[/math].

[J.branco]

ok, but my refering to the axis of symmetry of a fuction and its inverse.