# Composite functions

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I can't think of an example to prove that if then also note that

the problem is that no matter what i can think of it never works. I can sub g for f and say that f(g(x)) or g(f(x)) but as long as the question says that f and g are the same then i can't see how there'd ever be an example to prove this wrong.

I thought maybe that the statement was in the form if P then Q so i thought maybe that P does not imply Q but however it is Q implies P but i dont' quite fully understand the implies stuff so i don't even know if that's the right way to go.

the problem is that no matter what i can think of it never works. I can sub g for f and say that f(g(x)) or g(f(x)) but as long as the question says that f and g are the same then i can't see how there'd ever be an example to prove this wrong.

I thought maybe that the statement was in the form if P then Q so i thought maybe that P does not imply Q but however it is Q implies P but i dont' quite fully understand the implies stuff so i don't even know if that's the right way to go.

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#2

(Original post by

I can't think of an example to prove that if then also note that

the problem is that no matter what i can think of it never works. I can sub g for f and say that f(g(x)) or g(f(x)) but as long as the question says that f and g are the same then i can't see how there'd ever be an example to prove this wrong.

I thought maybe that the statement was in the form if P then Q so i thought maybe that P does not imply Q but however it is Q implies P but i dont' quite fully understand the implies stuff so i don't even know if that's the right way to go.

**will'o'wisp2**)I can't think of an example to prove that if then also note that

the problem is that no matter what i can think of it never works. I can sub g for f and say that f(g(x)) or g(f(x)) but as long as the question says that f and g are the same then i can't see how there'd ever be an example to prove this wrong.

I thought maybe that the statement was in the form if P then Q so i thought maybe that P does not imply Q but however it is Q implies P but i dont' quite fully understand the implies stuff so i don't even know if that's the right way to go.

If then

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I was supposed to prove this is an incorrect statement.

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#4

(Original post by

sorry my bad, i think it and don't write it out correctly, lol if only i could just contrapositive this and it'd be all right, sorry about the mess.

I was supposed to prove this is an incorrect statement.

**will'o'wisp2**)sorry my bad, i think it and don't write it out correctly, lol if only i could just contrapositive this and it'd be all right, sorry about the mess.

I was supposed to prove this is an incorrect statement.

and if and if (dunno how to write g piecewise atm on this, but you get the function) then both give and both are . Reversing this order, clearly we do not get an implication like the question says.

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(Original post by

Just pick a counter example.

and if and if (dunno how to write g piecewise atm on this, but you get the function) then both give and both are . Reversing this, clearly we do not get an implication like the question says.

**RDKGames**)Just pick a counter example.

and if and if (dunno how to write g piecewise atm on this, but you get the function) then both give and both are . Reversing this, clearly we do not get an implication like the question says.

i think you use the code called cases to produce them big squigly {} and write it kinda like a matrix

But ye f and g gotta be the same

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#7

(Original post by

ye but f and g must be the same

i think you use the code called cases to produce them big squigly {} and write it kinda like a matrix

But ye f and g gotta be the same

**will'o'wisp2**)ye but f and g must be the same

i think you use the code called cases to produce them big squigly {} and write it kinda like a matrix

But ye f and g gotta be the same

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#9

(Original post by

Product? No, the title says composite so you stuff one into itself.

**RDKGames**)Product? No, the title says composite so you stuff one into itself.

Personally, I wouldn't agree the above assertion is true because it allows ambiguous notation.

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#10

(Original post by

I dunno, but saying seems a to 'go against' function notation, where, as far as I'm aware, the argument of a function is written next to function inside brackets, eg., etc.

Personally, I wouldn't agree the above assertion is true because it allows ambiguous notation.

**Desmos**)I dunno, but saying seems a to 'go against' function notation, where, as far as I'm aware, the argument of a function is written next to function inside brackets, eg., etc.

Personally, I wouldn't agree the above assertion is true because it allows ambiguous notation.

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#11

**Desmos**)

I dunno, but saying seems a to 'go against' function notation, where, as far as I'm aware, the argument of a function is written next to function inside brackets, eg., etc.

Personally, I wouldn't agree the above assertion is true because it allows ambiguous notation.

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#12

(Original post by

The standard composite function notation shortens it from to , the same for . If it's anything other than this, the question's context would clarify on it.

**RDKGames**)The standard composite function notation shortens it from to , the same for . If it's anything other than this, the question's context would clarify on it.

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(Original post by

Do they? Where does it say that? The statement says that IF ff(x)=gg(x) THEN f(x)=g(x) but if you use my example above, we get the 'IF' condition, but it doesn't lead us to the 'THEN' condition, hence the statement is false as the 'IF' doesn't imply the 'THEN'

**RDKGames**)Do they? Where does it say that? The statement says that IF ff(x)=gg(x) THEN f(x)=g(x) but if you use my example above, we get the 'IF' condition, but it doesn't lead us to the 'THEN' condition, hence the statement is false as the 'IF' doesn't imply the 'THEN'

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#15

(Original post by

So if I write two functions without any gaps, eg., , then I'm referring to not

**Desmos**)So if I write two functions without any gaps, eg., , then I'm referring to not

*shorthand*and we were omitting arguments anyway I'd normally read as . But written as I'd interpret it as . I'm personally not a fan of it though.

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#16

(Original post by

depends on the context. If it was in

**_gcx**)depends on the context. If it was in

*shorthand*and we were omitting arguments anyway I'd normally read as . But written as I'd interpret it as . I'm personally not a fan of it though.
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#17

(Original post by

Is there any other notation where the context can change what it means?

**Desmos**)Is there any other notation where the context can change what it means?

might mean the complex conjugate of f, the adjoint function, the dual function, the function with removable singularities removed, the function f restricted to the interior of a given domain, the function f induces on a quotient space, etc...

That said, I agree with your concern in this case; I really don't like ff(x) here. All the same, I don't think it's worth derailing the thread over.

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#18

(Original post by

All the same, I don't think it's worth derailing the thread over.

**DFranklin**)All the same, I don't think it's worth derailing the thread over.

Btw, if the question has been answered satisfactorily, is it okay to then derail the thread?

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#19

(Original post by

Sorry about that. It's a bit easy to get carried away sometimes. :/ Next time I'll try to reel it in a bit.

Btw, if the question has been answered satisfactorily, is it okay to then derail the thread?

**Desmos**)Sorry about that. It's a bit easy to get carried away sometimes. :/ Next time I'll try to reel it in a bit.

Btw, if the question has been answered satisfactorily, is it okay to then derail the thread?

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