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inverse functions

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?

(edited 2 years ago)

Reply 1

mqb2766

Original post by Htx_x346

Can you upload a pic of the slide?

Reply 2

Htx_x346

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.?

Reply 3

mqb2766

Original post by Htx_x346

er not really...i can put a link to the slides though and tell you the slide no.?

sure

Reply 4

Htx_x346

Original post by mqb2766

sure

k it's slide 25 I think? it's 'Further example'
https://www.drfrostmaths.com/resource.php?rid=303

Reply 5

RichE

Original post by Htx_x346

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.

(edited 2 years ago)

Reply 6

Htx_x346

Original post by mqb2766

sure

slide 28, part c of the question, sorry

(edited 2 years ago)

Reply 7

Htx_x346

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

Reply 8

mqb2766

Original post by Htx_x346

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.

(edited 2 years ago)

Reply 9

Htx_x346

Original post by mqb2766

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

Reply 10

mqb2766

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

(edited 2 years ago)

Reply 11

Htx_x346

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

Reply 12

mqb2766

Original post by Htx_x346

hmmm

Think about the graphs of ln() and exp() or ... they're reflections in y=x.

Reply 13

RichE

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)

(edited 2 years ago)

Reply 14

Htx_x346

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

(edited 2 years ago)

Reply 15

Htx_x346

Original post by RichE

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

wait wdum?

Reply 16

RichE

Original post by Htx_x346

wait wdum?

Can you expand somewhat?

Reply 17

Htx_x346

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)