Math help (1 Viewer)

Fawun · Aug 23, 2012

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

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

I did do that. Look at the first step.

D94 said:
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?:
$-x+6$

I can't tell whether this is a rhetorical question or not but
$-x+6$
$-(x-6)$

I can factorise though.

twinklegal19 said:
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. $\frac{x^3}{x}$ or $\frac{x^3}{\sin{x}}$

similarly an even function divided by an even function is EVEN (positive divided by positive is still positive e.g. $\frac{x^4}{x^2+1}$

and an odd function divided by an even function, or an even function divided by an odd function is always ODD (e.g. $\frac{x^3}{\cos{x}}$

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/substracting odd and even functions (only multiply/dividing)

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)

I understood your paragraph but how can you determine whether the top and bottom are even/odd?

kazemagic · Aug 23, 2012

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

twinklegal19 said:
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. $\frac{x^3}{x}$ or $\frac{x^3}{\sin{x}}$

similarly an even function divided by an even function is EVEN (positive divided by positive is still positive e.g. $\frac{x^4}{x^2+1}$

and an odd function divided by an even function, or an even function divided by an odd function is always ODD (e.g. $\frac{x^3}{\cos{x}}$

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/substracting odd and even functions (only multiply/dividing)

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)

that 2nd last line is confusing lol

kazemagic · Aug 23, 2012

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

Fawun said:
I did do that. Look at the first step.

I can't tell whether this is a rhetorical question or not but
$-x+6$
$-(x-6)$

I can factorise though.

I understood your paragraph but how can you determine whether the top and bottom are even/odd?

nvm

twinklegal19 · Aug 23, 2012

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

Fawun said:
I did do that. Look at the first step.

I can't tell whether this is a rhetorical question or not but
$-x+6$
$-(x-6)$

I can factorise though.

I understood your paragraph but how can you determine whether the top and bottom are even/odd?

well I guess you can visualise them? like just imagine what the graph looks like and whether it has a symmetry around the y axis (x^2, x^4, x^2+1, x^2 + a constant etc), or a point symmetry (you can rotate it at the ORIGIN 180 degrees and it still looks the same, like x^3, x, sinx, 1/x)

dammit, I should be in bed...

Parvee · Aug 23, 2012

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

kazemagic said:
im pretty sure it's -(-x-6) lol

not sure if srs.

Fawun · Aug 23, 2012

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

kazemagic said:
im pretty sure it's -(-x-6) lol

I'm pretty sure it isn't lol. You need to go back to year 7 or 8

Fawun · Aug 23, 2012

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

twinklegal19 said:
well I guess you can visualise them? like just imagine what the graph looks like and whether it has a symmetry around the y axis (x^2, x^4, x^2+1, x^2 + a constant etc), or a point symmetry (you can rotate it at the ORIGIN 180 degrees and it still looks the same, like x^3, x, sinx, 1/x)

dammit, I should be in bed...

graphs? what graphs? Sy was talking about graphs before but I had no idea what he was saying because he was confusing me.

twinklegal19 · Aug 23, 2012

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

kazemagic said:
that 2nd last line is confusing lol

my bad

basically

ODD + ODD = ODD
EVEN + EVEN = EVEN
but ODD + EVEN = ? (it doesn't work)

kazemagic · Aug 23, 2012

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

my eyes playing tricks on me

thought the original equation was (x+6)

twinklegal19 · Aug 23, 2012

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

sorry if I'm confusing you, just ignore me then lol

Parvee · Aug 23, 2012

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

twinklegal19 said:
sorry if I'm confusing you, just ignore me then lol

I think you should remember shes only in yr10

kazemagic · Aug 23, 2012

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

twinklegal19 said:
my bad

basically

ODD + ODD = ODD
EVEN + EVEN = EVEN
but ODD + EVEN = ? (it doesn't work)

O i c

Parvee · Aug 23, 2012

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

Fawun said:
I

$f(-x) = \frac{-x+1}{x^2+1}$

$f(-x) =- \frac{x+1}{x^2+1}$

which therefore equals to -f(x) right?

Have you noticed what you did wrong?

D94 · Aug 23, 2012

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

Fawun said:
I can't tell whether this is a rhetorical question or not but
$-x+6$
$-(x-6)$

I can factorise though.

Alright, good. So for this equation:

$f(x) = \frac{x+1}{x^2+1}$

Now, -f(x) means -1 times the function:

$-f(x) = -1(\frac{x+1}{x^2+1})$

$-f(x) = \frac{-(x+1)}{x^2+1}$

$-f(x) = \frac{-x-1}{x^2+1}$

they all mean the same thing.

If we want to find f(-x), we just replace (x) with (-x), so we get:
$f(-x) = \frac{(-x)+1}{(-x)^2+1}$

and then we simplify and factorise

$f(-x) = \frac{-(x-1)}{(-x)^2+1}$
$f(-x) = \frac{-(x-1)}{(x)^2+1}$
which doesn't equal -f(x).

If we take f(-x) and the answer resolves back to f(x) then it's even.
If we take f(-x) and the answer resolves to -f(x) then it's odd.
Otherwise, it's neither.

Sy123 · Aug 23, 2012

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

Fawun said:
graphs? what graphs? Sy was talking about graphs before but I had no idea what he was saying because he was confusing me.

Well didnt your teacher tell you that, that is what even and odd functions are?
Odd functions are functions which where if you rotate about the origin 180 degrees, then you still have the original function, that is the definition of an odd function Even functions are functions symetrical about the y-axis.

These functions have the properties f(x)=f(-x) (EVEN)
f(-x)=-f(x) (ODD)

But what is your problem right now with the functions, I think that needs to be clarified first.

Fawun · Aug 24, 2012

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

D94 said:
Alright, good. So for this equation:

$f(x) = \frac{x+1}{x^2+1}$

Now, -f(x) means -1 times the function:

$-f(x) = -1(\frac{x+1}{x^2+1})$

$-f(x) = \frac{-(x+1)}{x^2+1}$

$-f(x) = \frac{-x-1}{x^2+1}$

they all mean the same thing.

If we want to find f(-x), we just replace (x) with (-x), so we get:
$f(-x) = \frac{(-x)+1}{(-x)^2+1}$

and then we simplify and factorise

$f(-x) = \frac{-(x-1)}{(x)^2+1}$

which doesn't equal -f(x).

If we take f(-x) and the answer resolves back to f(x) then it's even.
If we take f(-x) and the answer resolves to -f(x) then it's odd.
Otherwise, it's neither.

How come you only put a negative for the numerator?

So suppose I have this question:

$f(x) = \frac{1+2x}{x}$

Is this correct?

$f(-x) = \frac{1-2x}{-x}$

RivalryofTroll · Aug 24, 2012

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

Fawun said:
How come you only put a negative for the numerator?

So suppose I have this question:

$f(x) = \frac{1+2x}{x}$

Is this correct?
$f(-x) = \frac{1-2x}{-x}$

yep.

deswa1 · Aug 24, 2012

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

Fawun said:
How come you only put a negative for the numerator?

So suppose I have this question:

$f(x) = \frac{1+2x}{x}$

Is this correct?

$f(-x) = \frac{1-2x}{-x}$

Note that (-x)^2=x^2 as the squaring removes the negative -> this is why the denominator didn't change. And yes, your example is correct

Fawun · Aug 24, 2012

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

deswa1 said:
Note that (-x)^2=x^2 as the squaring removes the negative -> this is why the denominator didn't change. And yes, your example is correct

So how does this work?

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

$f(x) = x^3+5$
$f(-x) = (-x)^3+5$
$f(-x) = -x^3+5$

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

but the answer to that question is neither. NOTICE THAT $(-x)^3$ is equal to $-x^3$

However, for question d, the answer was:

$f(x) = x^4+10$
$f(-x) = (-x)^4+10$
$f(-x) = x^4+10$

therefore it's even.

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

Also, for my example, what do I do next? How do I know whether it's an odd or an even function? Do I like factorise it or something?

D94 · Aug 24, 2012

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

Fawun said:
How come you only put a negative for the numerator?

So suppose I have this question:

$f(x) = \frac{1+2x}{x}$

Is this correct?

$f(-x) = \frac{1-2x}{-x}$

It should also have a negative sign, but when you simplify (-x)², it goes back to x².

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