Math help (3 Viewers)

[Carrotsticks]

Re: Math help (Because Carrot made me do this)

Fabulous bedsheet design you've got going there.

 

[kazemagic]

Re: Math help (Because Carrot made me do this)

Fabulous bedsheet design you've got going there.

ofc

 

[Fawun]

Re: Math help (Because Carrot made me do this)

Some things are better explain irl.

How come the middle has a different function to the right and the left?

I just expanded what you gave me as f(-x)

If f(-x)=-x(-x-1)
f(-x)=x^2+x

When we sub in -x, its like subbing in any other pronumeral, for example

f(x)=x(x-1)
f(a)=a(a-1)


Putting a minus in front of the function means this -f(x)
So if

Now lets have a look at -f(x), does it look identical to anything? No, therefore its not odd
Does f(-x) look like anything? No, therefore it isnt even either.

Also me explaining what carrot said was a failure on my part. But basically yeah if f(-x)=-f(x) then its odd

Oh okay I see. So whenever I test whether a function is odd, even or neither, do I ALWAYS use -f(x) or f(-x)? or will I get the same answer if I use either of them?

 

[Carrotsticks]

Re: Math help (Because Carrot made me do this)

How come the middle has a different function to the right and the left?

Oh okay I see. So whenever I test whether a function is odd, even or neither, do I ALWAYS use -f(x) or f(-x)? or will I get the same answer if I use either of them?

ALWAYS use f(-x) and see what happens from there.

Well I can't use the same function for all of them because (as far as you know atm) there isn't a function that can satisfy all three.

So of course I would have to use different functions.

 

[kazemagic]

Re: Math help (Because Carrot made me do this)

How come the middle has a different function to the right and the left?




Oh okay I see. So whenever I test whether a function is odd, even or neither, do I ALWAYS use -f(x) or f(-x)? or will I get the same answer if I use either of them?

u ALWAYS have to use f(-x) not -f(x). -f(x) is just the result u get by using f(-x) IF the function is odd

 

[Sy123]

Re: Math help (Because Carrot made me do this)

How come the middle has a different function to the right and the left?




Oh okay I see. So whenever I test whether a function is odd, even or neither, do I ALWAYS use -f(x) or f(-x)? or will I get the same answer if I use either of them?

To test for even or odd functions follow Carrot's design, you always have to use f(-x) to see what you get, whether it equals to f(x) or -f(x) determines even or oddness (or neither of them if none of them apply)

 

[Fawun]

Re: Math help (Because Carrot made me do this)

for ii), you said -f(x) = odd. Is f(-x) odd as well or?

Also for the f(x) = x^3-3x, you put the minus outside the bracket, isn't it suppose to be inside the bracket? How come the one on the left is x cubed whilst the one on the right is x squared? lol your I can't read your handwriting.

 

[kazemagic]

Re: Math help (Because Carrot made me do this)

for ii), you said -f(x) = odd. Is f(-x) odd as well or?

Also for the f(x) = x^3-3x, you put the minus outside the bracket, isn't it suppose to be inside the bracket? How come the one on the left is x cubed whilst the one on the right is x squared? lol your I can't read your handwriting.

Ye screwed that one up, its supposed to go like this:
f(x)=x^3-3x
f(-x)= (-x)^3 times -3(-x)
= -x^3+3x
= -(x^3-3x)
= -f(x)
therefore it is odd

 

[kazemagic]

Re: Math help (Because Carrot made me do this)

for ii), you said -f(x) = odd. Is f(-x) odd as well or?

Also for the f(x) = x^3-3x, you put the minus outside the bracket, isn't it suppose to be inside the bracket? How come the one on the left is x cubed whilst the one on the right is x squared? lol your I can't read your handwriting.

f(-x) basically means to sub in a negative pronumeral. Once u subbed in that negative pronumeral, and u get -f(x), that means the function is odd. If u sub in a neg pronumeral into a function and it stays the same (aka f(x)), it is an even function

f(-x) is not always the same as -f(x) so for ur above question f(-x) is not an odd, its not anything. f(-x) just means ur subbing a negative pronumeral into it to determine whether the function is odd, even or neither based on the results u get

 

[Fawun]

Re: Math help (Because Carrot made me do this)

Ye screwed that one up, its supposed to go like this:
f(x)=x^3-3x
f(-x)= (-x)^3 times -3(-x)
= -x^3+3x
= -(x^3-3x)
= -f(x)
therefore it is odd

Okay I think I understand it a bit (lol after all that work and posts). I'll try and do a question on my own.

So the question is:



So this is how I do it:




So then what happens next? there's a minus in front of the x in the numerator so does that mean it's odd?

 

[kazemagic]

Re: Math help (Because Carrot made me do this)

Okay I think I understand it a bit (lol after all that work and posts). I'll try and do a question on my own.

So the question is:



So this is how I do it:




So then what happens next? there's a minus in front of the x in the numerator so does that mean it's odd?

yes its an odd
EDIT: Its neither. my bad

 

[Carrotsticks]

Re: Math help (Because Carrot made me do this)

Okay I think I understand it a bit (lol after all that work and posts). I'll try and do a question on my own.

So the question is:



So this is how I do it:




So then what happens next? there's a minus in front of the x in the numerator so does that mean it's odd?

Well compare it with f(x).

Is it the same as f(x)? No.

Is it the same as -f(x)? No.

Therefore, neither.

 

[Fawun]

Re: Math help (Because Carrot made me do this)

Well compare it with f(x).

Is it the same as f(x)? No.

Is it the same as -f(x)? No.

Therefore, neither.

Why can't you do:



So that it becomes an odd since -f(x)?

Also, this is MY working out for question c in the textbook:





Therefore it's odd because there's a minus in front right?

but the answer to that question is neither. NOTICE THAT is equal to

However, for question d, the answer was:





therefore it's even.

What? how did the -x^4 turn into positive but before the -x^3 turned into a negative?

 

[Carrotsticks]

Re: Math help (Because Carrot made me do this)

Okay I found your problem.

You are getting f(-x) mixed up with -f(x).

Suppose I have this:



Can you tell me what you think -f(x) is.

 

[Fawun]

Re: Math help (Because Carrot made me do this)

Okay I found your problem.

You are getting f(-x) mixed up with -f(x).

Suppose I have this:



Can you tell me what you think -f(x) is.

I'd only be able to go as far as:



before not knowing what to do and looking at BOB.

or maybe I put the minus in front so that it looks like this:



which therefore equals to -f(x) right?

 

[Carrotsticks]

Re: Math help (Because Carrot made me do this)

I'd only be able to go as far as:



before not knowing what to do and looking at BOB.

or maybe I put the minus in front so that it looks like this:



which therefore equals to -f(x) right?

That's where the mistake is, your second one. See you you had f(-x) = - etc etc? What you did was just throw a - sign in front. But that is NOT f(-x).

Doing that is -f(x).

 

[Fawun]

Re: Math help (Because Carrot made me do this)

That's where the mistake is, your second one. See you you had f(-x) = - etc etc? What you did was just throw a - sign in front. But that is NOT f(-x).

Doing that is -f(x).

Wait idgi. Was throwing a - sign in front the right thing to do? what do I need to do after?

 

[D94]

Re: Math help (Because Carrot made me do this)

I'd only be able to go as far as:



before not knowing what to do and looking at BOB.

or maybe I put the minus in front so that it looks like this:



which therefore equals to -f(x) right?

No.

TBH, I think the problem lies in your basic factorisation skills. Because you may not have had a good start to factorisation, maybe you only rote learned it in your early years, you seem to just miss out on the factorisation step. The issue won't be resolved if your basic, core knowledge and skills aren't there. Otherwise, you'd just be rote learning, which won't help you in the exam.

Can you factorise the following expression by taking out -1 as a factor?:

 

[Parvee]

Re: Math help (Because Carrot made me do this)

Wait idgi. Was throwing a - sign in front the right thing to do? what do I need to do after?

Basically your meant to sub in -x wherever the x is.

 

[twinklegal19]

Re: Math help (Because Carrot made me do this)

think of it this way

treat "ODD" like it's a negative number and "EVEN" like it's positive

say a negative number divided by a negative number is positive, right? So an odd function divided by an odd function is EVEN (e.g.

similarly an even function divided by an even function is EVEN (positive divided by positive is still positive e.g.

and an odd function divided by an even function, or an even function divided by an odd function is always ODD (e.g.

A positive number + a positive number is always a positive number, so

EVEN + EVEN = EVEN

and a negative number + a negative number is always negative

therefore ODD + ODD = ODD

so what does a positive number plus a negative number equal to? Well we have no clue, since it can be anything, therefore this doesn't work for adding/subtracting both odd and even functions.

I guess you can use this to check your answers (if you can quickly determine whether the top and bottom are even/odd, it helps if you can visualise them separately)