F(-x) is a reflection over the y axis -f(x)

  1. f(-x) is a reflection over the y axis
    -f(x) is a reflection over the x axis

    Now, how do we represent a reflection over y=x?
     
    Last edited: Dec 6, 2013
  2. jcsd
  3. Its [itex] f^{-1}(x) [/itex]
    Very beautiful!
     
  4. Mark44

    Staff: Mentor

    If (x, y) is a point on the graph of f, (y, x) will be the reflection of that point across the line y = x.

    What if f doesn't have an inverse? For example, y = f(x) = x2. This function is not one-to-one, so doesn't have an inverse.
     
  5. If a function is not one to one,then there is no function that is its inverse.But there is of course a relation which is the function's inverse.And that relation can be ploted.For [itex]y=x^2 [/itex] we have [itex] x=\pm \sqrt{y} [/itex]which is a two-valued relation between x and y.
     
  6. Mark44

    Staff: Mentor

    Understood. My point was that you can't refer to it as f-1(x).
     
  7. Every function is a relation. If ##R## is a relation, then ##R^{-1}## is a well-defined relation.
     
  8. Okay, now how about a reflection over y = -x?
     
  9. Let's see...a reflection over line y=-x means [itex] (x_0,y_0)\rightarrow(-y_0,-x_0) [/itex].
    It think it should be [itex]-f^{-1}(-x)[/itex]...ohh...sorry...[itex]-R^{-1}(-x) [/itex].
     
  10. Yeah, makes sense...
    Thanks :biggrin:
     
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