# even odd functions

• Jan 9th 2007, 12:37 PM
qbkr21
even odd functions
1. For each of the following functions, decide whether it is even, odd, or neither. Enter E for an EVEN function, O for an ODD function and N for a function which is NEITHER even nor odd.

A. f(x)= x^3+x^5+x^7
B. f(x)= (-5x^2)-(3x^4)-2
C. f(x)= (x^2)+(3x^4)-2
D. f(x)= x^-2
• Jan 9th 2007, 01:10 PM
topsquark
Quote:

Originally Posted by qbkr21
1. For each of the following functions, decide whether it is even, odd, or neither. Enter E for an EVEN function, O for an ODD function and N for a function which is NEITHER even nor odd.

A. f(x)= x^3+x^5+x^7
B. f(x)= (-5x^2)-(3x^4)-2
C. f(x)= (x^2)+(3x^4)-2
D. f(x)= x^-2

The definition of an even function is that f(-x) = f(x), and an odd function has the property f(-x) = -f(x).

So for A: $f(-x) = (-x)^3 + (-x)^5 + (-x)^7 = -x^3 - x^5 - x^7 = -f(x)$. So A is an odd function.

B: $f(-x) = -5(-x)^2 - 3(-x)^4 - 2 = -5x^2 - 3x^4 -2 = f(x)$ so this function is even.

You should be able to do C and D by yourself. (They are both even.)

-Dan
• Jan 9th 2007, 01:13 PM
qbkr21
Sir I think that one of these is incorrect could you please recheck the problem. Thanks
• Jan 9th 2007, 01:22 PM
topsquark
Quote:

Originally Posted by qbkr21
Sir I think that one of these is incorrect could you please recheck the problem. Thanks

(Shrugs) Which one do you think is wrong?

Quote:

Originally Posted by topsquark
The definition of an even function is that f(-x) = f(x), and an odd function has the property f(-x) = -f(x).

So for A: $f(-x) = (-x)^3 + (-x)^5 + (-x)^7 = -x^3 - x^5 - x^7 = -f(x)$. So A is an odd function.

B: $f(-x) = -5(-x)^2 - 3(-x)^4 - 2 = -5x^2 - 3x^4 -2 = f(x)$ so this function is even.

You should be able to do C and D by yourself. (They are both even.)

-Dan

C: $f(-x) = (-x)^2 + 3(-x)^4 -2 = x^2 + 3x^4 - 2 = f(x)$ so this is even.

D: $f(-x) = \frac{1}{(-x)^2} = \frac{1}{x^2} = f(x)$ so this is even.

I note that B and C are fairly similar. Is there possibly a typo?

-Dan
• Jan 9th 2007, 01:29 PM
qbkr21
My Fault it, here I will try typing it in through Latex...

A.

$f(x)=x^3+x^5+x^7$

B.

$f(x)=-5x^2-3x^4-2$

C.

$f(x)=x^2+3x^4+2x^7$

D.

f(x)=x^-2

Sorry Again, hope this makes a bit easier.
• Jan 9th 2007, 01:33 PM
topsquark
Quote:

Originally Posted by qbkr21
My Fault it, here I will try typing it in through Latex...

A.

$f(x)=x^3+x^5+x^7$

B.

$f(x)=-5x^2-3x^4-2$

C.

$x^2+3x^4+2x^7$

D.

X^-2

Sorry Again, hope this makes a bit easier.

Okay, so the problem is with C. Let's try this again:
$f(-x) = (-x)^2 + 3(-x)^4 + 2(-x)^7 = x^2 + 3x^4 - 2x^7 \neq f(x), -f(x)$

Since f(-x) is equal to neither f(x) nor -f(x), this function is a "neither." (Or in more advanced language, is not a "parity eigenstate.")

-Dan
• Jan 9th 2007, 01:34 PM
qbkr21
Thanks Dan I appreciate the help. Things are worked out now
• Jan 9th 2007, 01:48 PM
topsquark
Quote:

Originally Posted by qbkr21
Thanks Dan I appreciate the help. Things are worked out now

Always pleased to be of service! :)

-Dan