Math help (3 Viewers)
- Thread starter Fawun
- Start date
Carrotsticks
Retired
- Joined
- Jun 29, 2009
- Messages
- 9,494
- Gender
- Undisclosed
- HSC
- N/A
Re: Math help (Because Carrot made me do this)
 = \frac{x}{x^2+2}\\\\ f(-x) = \frac{-x}{x^2+2} = - f(x) )
Therefore odd.
Just make f(x) become f(-x) and look at what happens to the function.
It it's the exact same thing, then even.
If the same thing, but with a minus in front (like here), then odd.
If neither, then neither.
Classify the following functions f(x) as odd, even or neither.
What do I do?
Therefore odd.
Just make f(x) become f(-x) and look at what happens to the function.
It it's the exact same thing, then even.
If the same thing, but with a minus in front (like here), then odd.
If neither, then neither.
Re: Math help (Because Carrot made me do this)
2 things u need to rmbr
Even functions:
f(-x)=f(x) (when subbed in a negative pronumeral, the equation still stays the same)
Odd functions:
f(-x)=-f(x) (when subbed in a negative pronumeral, the equation becomes negative)
Wow ur going fast, last time i saw u, u were doing quadratics
2 things u need to rmbr
Even functions:
f(-x)=f(x) (when subbed in a negative pronumeral, the equation still stays the same)
Odd functions:
f(-x)=-f(x) (when subbed in a negative pronumeral, the equation becomes negative)
Wow ur going fast, last time i saw u, u were doing quadratics
Re: Math help (Because Carrot made me do this)
what? where?
Why did you put the minus sign in front of the x but not for the x squared part of the denominator?
Therefore odd.
Just make f(x) become f(-x) and look at what happens to the function.
It it's the exact same thing, then even.
If the same thing, but with a minus in front (like here), then odd.
If neither, then neither.
Carrotsticks
Retired
- Joined
- Jun 29, 2009
- Messages
- 9,494
- Gender
- Undisclosed
- HSC
- N/A
Re: Math help (Because Carrot made me do this)
Because if I replace the x with -x, then I get (-x)^2, which is still x^2.
Re: Math help (Because Carrot made me do this)
If the function is the same as the question, then it's even
If it's different from the question, then it's odd
Am I right?
Okay so let me get this straight.
If the function is the same as the question, then it's even
If it's different from the question, then it's odd
Am I right?
Carrotsticks
Retired
- Joined
- Jun 29, 2009
- Messages
- 9,494
- Gender
- Undisclosed
- HSC
- N/A
Re: Math help (Because Carrot made me do this)
If I replace X with (-X) and I get the exact same thing, then it's even.
If I replace X with (-X) and I get the same thing EXCEPT it has minus in front, then it's odd.
If I replace X with (-X) and I get neither of the above cases, then it is neither.
Not really.
If I replace X with (-X) and I get the exact same thing, then it's even.
If I replace X with (-X) and I get the same thing EXCEPT it has minus in front, then it's odd.
If I replace X with (-X) and I get neither of the above cases, then it is neither.
Re: Math help (Because Carrot made me do this)
When subbed in a negative pronumeral, and the equation stays the same and becomes negative, it is an odd
When subbed in a negative pronumeral, and the equation becomes something different, it is neither
fawun bro why dont u listen to ur teacher during class time
When subbed in a negative pronumeral, and the equations stays the same, it is an even
When subbed in a negative pronumeral, and the equation stays the same and becomes negative, it is an odd
When subbed in a negative pronumeral, and the equation becomes something different, it is neither
fawun bro why dont u listen to ur teacher during class time
Re: Math help (Because Carrot made me do this)
When will there be a case where it will be a neither? doesn't a question have to have a plus or a minus? idgi.
So let's say for this question:
)
I got:
 = x(x-1))
 = -x(-x-1))
Is this right so far? What do I do next? Do I like expand it or something?
In front of where? the x? or any number with a minus in front?
When will there be a case where it will be a neither? doesn't a question have to have a plus or a minus? idgi.
So let's say for this question:
I got:
Is this right so far? What do I do next? Do I like expand it or something?
Re: Math help (Because Carrot made me do this)
Okay I understood those parts thanks. She explains things too quickly and i'm too embarrassed to ask a question since everyone else is smarter than me and will think i'm dumb lol.
Carrotsticks
Retired
- Joined
- Jun 29, 2009
- Messages
- 9,494
- Gender
- Undisclosed
- HSC
- N/A
Re: Math help (Because Carrot made me do this)
So for example if:
 = \frac{x}{1+x^2})
Then -f(x) is:
 = - \frac{x}{1+x^2} = \frac{-x}{1+x^2})
In your case, you have
 = -x(-x-1) = x(x+1))
But notice, that's NOT the original function. On top of that it's NOT the same thing as the original function, but with a -1 chucked in front of it:
 = -x(x-1) $ which is NOT the same thing as what you have $ x(x+1) )
So therefore, not odd and not even, and thus neither.
When I say it has a minus in front, I mean that it's the EXACT same function, but multiplied by -1.In front of where? the x? or any number with a minus in front?
When will there be a case where it will be a neither? doesn't a question have to have a plus or a minus? idgi.
So let's say for this question:
I got:
Is this right so far? What do I do next? Do I like expand it or something?
So for example if:
Then -f(x) is:
In your case, you have
But notice, that's NOT the original function. On top of that it's NOT the same thing as the original function, but with a -1 chucked in front of it:
So therefore, not odd and not even, and thus neither.
Sy123
This too shall pass
- Joined
- Nov 6, 2011
- Messages
- 3,730
- Gender
- Male
- HSC
- 2013
Re: Math help (Because Carrot made me do this)
=x^2-x \ \ \ f(-x)=x^2+x \\ \therefore f(x) \neq f(-x) \neq -f(x) )
Therefore function is neither. What classifies a function of being odd or even is:
If a function is odd, then if you rotate it 360 degrees about the origin, the function is the exact same
If a function is even, then it it symetrical about the y axis.
This is how people derive the rules for odd and even functions, you dont need to know how they did it, but you need to know why an even function is an even function. If we test whether f(x)=f(-x), if its true then function is symmetrical hence it is even.
If its neither, it has neither properties of an even or odd function.
When carrot means it has a minus in front, he means:
=x^3 \ \ f(-x)=-x^3 \ \ \ -f(x)=-x^3 )
Hence odd:
If we translate this:
If I replace X with (-X) and I get the same thing EXCEPT it has minus in front, then it's odd.
'If I replace x with (-x), i.e. evaluating f(-x), and I get the same thing [f(x)] but with a minus in front [-f(x)]'
You can do two things, expand:In front of where? the x? or any number with a minus in front?
When will there be a case where it will be a neither? doesn't a question have to have a plus or a minus? idgi.
So let's say for this question:
I got:
Is this right so far? What do I do next? Do I like expand it or something?
Therefore function is neither. What classifies a function of being odd or even is:
If a function is odd, then if you rotate it 360 degrees about the origin, the function is the exact same
If a function is even, then it it symetrical about the y axis.
This is how people derive the rules for odd and even functions, you dont need to know how they did it, but you need to know why an even function is an even function. If we test whether f(x)=f(-x), if its true then function is symmetrical hence it is even.
If its neither, it has neither properties of an even or odd function.
When carrot means it has a minus in front, he means:
Hence odd:
If we translate this:
If I replace X with (-X) and I get the same thing EXCEPT it has minus in front, then it's odd.
'If I replace x with (-x), i.e. evaluating f(-x), and I get the same thing [f(x)] but with a minus in front [-f(x)]'
Re: Math help (Because Carrot made me do this)
)
? Did you just cancel out the negatives? or did you expand it?
Why is it -f(x)? isn't it f(-x)?When I say it has a minus in front, I mean that it's the EXACT same function, but multiplied by -1.
So for example if:
Then -f(x) is:
How did you getIn your case, you have
Wait what? why did you chuck a -1 in front of it?But notice, that's NOT the original function. On top of that it's NOT the same thing as the original function, but with a -1 chucked in front of it:
So therefore, not odd and not even, and thus neither.
Carrotsticks
Retired
- Joined
- Jun 29, 2009
- Messages
- 9,494
- Gender
- Undisclosed
- HSC
- N/A
Re: Math help (Because Carrot made me do this)
I got the x(x+1) by multiplying the minus inside.
OKok here let me draw a diagram for you. Give me a few moments.
That's the idea. Since -f(x) IS equal to f(-x), then it is an odd function.Why is it -f(x)? isn't it f(-x)?
How did you get
Wait what? why did you chuck a -1 in front of it?
I got the x(x+1) by multiplying the minus inside.
OKok here let me draw a diagram for you. Give me a few moments.
Re: Math help (Because Carrot made me do this)
Why didn't you put a minus in front of the second function? I know that (-x)^2 is the same as x^2 but why didn't you put -x? so then it becomes x^2-x?You can do two things, expand:
So basically f(-x) is the same as -f(x)?When carrot means it has a minus in front, he means:
Sy123
This too shall pass
- Joined
- Nov 6, 2011
- Messages
- 3,730
- Gender
- Male
- HSC
- 2013
Re: Math help (Because Carrot made me do this)
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)
=(-x)((-x)-1) \\ f(-x)=-x(-x-1)= x^2+x )
Putting a minus in front of the function means this -f(x)
So if
=x(x-1) \\ $Times -1 to both sides$ \\ -f(x)= - [x(x-1)]=-x(x-1) )
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
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
Carrotsticks
Retired
- Joined
- Jun 29, 2009
- Messages
- 9,494
- Gender
- Undisclosed
- HSC
- N/A
Re: Math help (Because Carrot made me do this)
Some things are better explain irl.
Some things are better explain irl.
