1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

  1. Dec 6, 2013 #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. Dec 6, 2013 #2

    ShayanJ

    User Avatar
    Gold Member

    Its [itex] f^{-1}(x) [/itex]
    Very beautiful!
     
  4. Dec 6, 2013 #3

    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. Dec 6, 2013 #4

    ShayanJ

    User Avatar
    Gold Member

    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. Dec 6, 2013 #5

    Mark44

    Staff: Mentor

    Understood. My point was that you can't refer to it as f-1(x).
     
  7. Dec 6, 2013 #6
    Every function is a relation. If ##R## is a relation, then ##R^{-1}## is a well-defined relation.
     
  8. Dec 7, 2013 #7
    Okay, now how about a reflection over y = -x?
     
  9. Dec 7, 2013 #8

    ShayanJ

    User Avatar
    Gold Member

    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. Dec 7, 2013 #9
    Yeah, makes sense...
    Thanks :biggrin:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: F(-x) is a reflection over the y axis -f(x)
  1. Polar axis? (Replies: 1)

  2. Axis of a Parabola (Replies: 24)

Loading...