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

 P: 18 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?
 P: 771 Its $f^{-1}(x)$ Very beautiful!
Mentor
P: 21,215
 Quote by hb20007 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?
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.

 Quote by Shyan Its $f^{-1}(x)$ Very beautiful!
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.

P: 771
F(-x) is a reflection over the y axis -f(x)

 Quote by Mark44 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.
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 $y=x^2$ we have $x=\pm \sqrt{y}$which is a two-valued relation between x and y.
 Mentor P: 21,215 Understood. My point was that you can't refer to it as f-1(x).
Newcomer
P: 341
 Quote by Mark44 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.
Every function is a relation. If ##R## is a relation, then ##R^{-1}## is a well-defined relation.
 P: 18 Okay, now how about a reflection over y = -x?
 P: 771 Let's see...a reflection over line y=-x means $(x_0,y_0)\rightarrow(-y_0,-x_0)$. It think it should be $-f^{-1}(-x)$...ohh...sorry...$-R^{-1}(-x)$.
 P: 18 Yeah, makes sense... Thanks

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