- #1

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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?

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

Now, how do we represent a reflection over y=x?

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- Thread starter hb20007
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- #1

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

Now, how do we represent a reflection over y=x?

Last edited:

- #2

ShayanJ

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Its [itex] f^{-1}(x) [/itex]

Very beautiful!

Very beautiful!

- #3

Mark44

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-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.

What if f doesn't have an inverse? For example, y = f(x) = xIts [itex] f^{-1}(x) [/itex]

Very beautiful!

- #4

ShayanJ

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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) = x^{2}. 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 [itex]y=x^2 [/itex] we have [itex] x=\pm \sqrt{y} [/itex]which is a two-valued relation between x and y.

- #5

Mark44

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Understood. My point was that you can't refer to it as f^{-1}(x).

- #6

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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) = x^{2}. 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.

- #7

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Okay, now how about a reflection over y = -x?

- #8

ShayanJ

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It think it should be [itex]-f^{-1}(-x)[/itex]...ohh...sorry...[itex]-R^{-1}(-x) [/itex].

- #9

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Yeah, makes sense...

Thanks

Thanks

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