# odd and even function (1 Viewer)

#### kittyful

##### Member
i need help, i don't understand the concept of odd and even functions, i dont get it, when a question asks which is an odd or even how do i know if its odd or even, after i substituted f(x) any help... help with an example, would be nice

#### Tofuu

##### Member
even f(x)= f(-x)

odd f(-x)=-f(x)

neither is when non of the above cases are true

#### Tofuu

##### Member
even f(x)= f(-x)

odd f(-x)=-f(x)

neither is when non of the above cases are true

#### random-1006

##### Banned
i need help, i don't understand the concept of odd and even functions, i dont get it, when a question asks which is an odd or even how do i know if its odd or even, after i substituted f(x) any help... help with an example, would be nice

ok even function are symmetric about the y axis: the condition is that f(-x) = f(x), hopefully this result seems fairly obvious, if you have something symmtric about the y axis, if i go out 3 units right from the origin and i go 3 units left fro the origin i will get the same function value;

e.g. Show f(x) = x^4 - x^2 is an even function

f(-x) = (-x) ^4 - ( -x)^2 = x^4 -x^2= f(x), hence even

for odd functions we have rotational symmtry about the origin, the condition to show is f(-x) = -f(x)

e.g. show f(x) = x^3 - x^5 is odd
f(-x) = (-x)^3 - (-x)^5 = -x^3 - (-x^5) = - [x^3 -x^5] = -f(x)

i know my spelling is shit

these formulas have a strong geometric meaning behind them, look at what f(-x)= -f(x) is actually saying.

its saying that if i go a distance "x" left from the origin and get the function value, it will equal the negative ( ie a reflection over the x axis) of the function value if i go the equal distance in the right direction. Just thinking about this geometrically it should be obvious that i can rotate the graph 180 degrees about the origin and get the same thing.

Maths is not just about chanting "f(-x) = - f(x) " , if you understand what the formula is saying, you will NEVER forget it.

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#### 4025808

##### Well-Known Member
ok even function are symmetric about the y axis: the condition is that f(-x) = f(x), hopefully this result seems fairly obvious, if you have something symmtric about the y axis, if i go out 3 units right from the origin and i go 3 units left fro the origin i will get the same function value;

e.g. Show f(x) = x^4 - x^2 is an even function

f(-x) = (-x) ^4 - ( -x)^2 = x^4 -x^2= f(x), hence even

for odd functions we have rotational symmtry about the origin, the condition to show is f(-x) = -f(x)

e.g. show f(x) = x^3 - x^5 is odd
f(-x) = (-x)^3 - (-x)^5 = -x^3 - (-x^5) = - [x^3 -x^5] = -f(x)

i know my spelling is shit

these formulas have a strong geometric meaning behind them, look at what f(-x)= -f(x) is actually saying.

its saying that if i go a distance "x" left from the origin and get the function value, it will equal the negative ( ie a reflection over the x axis) of the function value if i go the equal distance in the right direction. Just thinking about this geometrically it should be obvious that i can rotate the graph 180 degrees about the origin and get the same thing.

Maths is not just about chanting "f(-x) = - f(x) " , if you understand what the formula is saying, you will NEVER forget it.

also to add, if you have doubts about an odd or neither function, then try factorizing the minus out of the function
if the f(-x) is not equal to -f(x) then you'll know it's neither...
and vice versa for the odd function...

but yeah you basically posted the best explanation out of the users :L

#### random-1006

##### Banned
also to add, if you have doubts about an odd or neither function, then try factorizing the minus out of the function
if the f(-x) is not equal to -f(x) then you'll know it's neither...
and vice versa for the odd function...

but yeah you basically posted the best explanation out of the users :L

what does that mean?, some of these emoticons are complete rubbish

#### MetroMattums

##### Member
what does that mean?, some of these emoticons are complete rubbish
:L means he's laughing bru

#### BloomyLove

##### HSC Hater
shouldn't be that hard, look at the examples in your text book.

If you have Mathsinfocus check out chaper 5 and you will need it chapter 8 as well.
Ahhhh... I have to finish Chapter 8 to submit when school comes back.

#### kittyful

##### Member
Normally, if a function has an odd power, then it is an odd function. Whereas if a function has a even power, it is an even function.

Eg: y=x is an odd function.
y=x^2 is an even function.

For questions that involve proving odd, even or neither funtions, just sub in -x wherever you see x.

So, if f(x)=2x^2

Then, f(-x)=2(-x)^2 = 2x^2
Therefore, f(x)=2x^2 is an even function.
yea i get that substituting thing ... but when you get 2x^2 how do you know that, that is an even function? do you always substitute in -x ?

#### kittyful

##### Member
thanks everyone for your suggestions it really helped

#### random-1006

##### Banned
yea i get that substituting thing ... but when you get 2x^2 how do you know that, that is an even function? do you always substitute in -x ?

f(-x)= 2(-x)^2= 2x^2= f(x), we have showed f(-x) = f(x), thus even

you always do f(-x), if you get f(-x)= f(x) its even. If you get f(-x)= -f(x), its odd. and if f(-x) does not equal f(x) or -f(x) its Neither

#### kittyful

##### Member
f(-x)= 2(-x)^2= 2x^2= f(x), we have showed f(-x) = f(x), thus even

you always do f(-x), if you get f(-x)= f(x) its even. If you get f(-x)= -f(x), its odd. and if f(-x) does not equal f(x) or -f(x) its Neither
ahh.. i get it ahha, thanks