# inverse functions

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#1
in the Dr F maths ppt it says that 'if the function is equal to its inverse, it must lie on the line y=x. f(x)=x. '

not tryna sound stupid but y=1/x is equal to its inverse but f(x) isn't equal to x?
Last edited by Htx_x346; 1 month ago
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1 month ago
#2
(Original post by Htx_x346)
in the Dr F maths ppt it says that 'if the function is equal to its inverse, it must lie on the line y=x. f(x)=x. '

not tryna sound stupid but y=1/x is equal to its inverse but f(x) isn't equal to x?
Can you upload a pic of the slide?
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#3
(Original post by mqb2766)
Can you upload a pic of the slide?
er not really...i can put a link to the slides though and tell you the slide no.?
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1 month ago
#4
(Original post by Htx_x346)
er not really...i can put a link to the slides though and tell you the slide no.?
sure
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#5
(Original post by mqb2766)
sure
k it's slide 25 I think? it's 'Further example'
https://www.drfrostmaths.com/resource.php?rid=303
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1 month ago
#6
(Original post by Htx_x346)
in the Dr F maths ppt it says that 'if the function is equal to its inverse, it must lie on the line y=x. f(x)=x. '

not tryna sound stupid but y=1/x is equal to its inverse but f(x) isn't equal to x?
I can't see the slides but this clearly isn't true as an identity. It needs to have reflective symmetry in the line y=x. For example f(x)=1-x is another such self-inverse function.
Last edited by RichE; 1 month ago
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#7
(Original post by mqb2766)
sure
slide 28, part c of the question, sorry
Last edited by Htx_x346; 1 month ago
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#8
(Original post by RichE)
I can't see the slides but this clearly isn't true. It needs to have reflective symmetry in the line y=x. For example f(x)=1-x is another such self-inverse function.
that's what i thought
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1 month ago
#9
(Original post by Htx_x346)
in the Dr F maths ppt it says that 'if the function is equal to its inverse, it must lie on the line y=x. f(x)=x. '

not tryna sound stupid but y=1/x is equal to its inverse but f(x) isn't equal to x?
From what I can see on the slide 26 (and the usual explanation) is f and f^(-1) are reflections in y-x line. The reciprocal you mention is a self inverse (involution) so its equal to its own reflection.

He says y-x is line of symmetry for f and its inverse.
Last edited by mqb2766; 1 month ago
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#10
(Original post by mqb2766)
From what I can see on the slide 26 (and the usual explanation) is f and f^(-1) are reflections in y-x line. The reciprocal you mention is a self inverse (involution) so its equal to its own reflection.

He says y-x is line of symmetry for f and its inverse.
oh i'm just being stupid..it meant you can equate f(x)=x when you're trying to find the intersection of f(x)=f^-1(x).
thanks
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1 month ago
#11
(Original post by Htx_x346)
oh i'm just being stupid..it meant you can equate f(x)=x when you're trying to find the intersection of f(x)=f^-1(x).
thanks
It just means f^(-1) s a reflection of f in the line y=x and vice versa.
The reflection of 1/x is 1/x hence the self inverse property or f(f(x)) = x
Last edited by mqb2766; 1 month ago
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#12
(Original post by mqb2766)
It just means f^(-1) s a reflection of f in the line y=x and vice versa.
The reflection of 1/x is 1/x hence the self inverse property or f(f(x)) = x
hmmm
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1 month ago
#13
(Original post by Htx_x346)
hmmm
Think about the graphs of ln() and exp() or ... they're reflections in y=x.
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1 month ago
#14
(Original post by Htx_x346)
oh i'm just being stupid..it meant you can equate f(x)=x when you're trying to find the intersection of f(x)=f^-1(x).
thanks
I imagine this is what's meant here for this specific function (which isn't self-inverse).

And in this case f(x)=x is a lot easier to solve than f(x)=f^(-1)(x)
Last edited by RichE; 1 month ago
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#15
(Original post by mqb2766)
Think about the graphs of ln() and exp() or ... they're reflections in y=x.
wait so was he wrong? I think i just confused myself even more
Last edited by Htx_x346; 1 month ago
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#16
(Original post by RichE)
I imagine this is what's meant here for this specific function (which isn't self-inverse).
wait wdum?
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1 month ago
#17
(Original post by Htx_x346)
wait wdum?
Can you expand somewhat?
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#18
(Original post by RichE)
Can you expand somewhat?
it's fine, this bit helped. I got it now, thanks x

(Original post by RichE)
I imagine this is what's meant here for this specific function (which isn't self-inverse).

And in this case f(x)=x is a lot easier to solve than f(x)=f^(-1)(x)
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