Math Help - even odd functions

1. 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

2. 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

3. Sir I think that one of these is incorrect could you please recheck the problem. Thanks

4. 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?

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

5. 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.

6. 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

7. Thanks Dan I appreciate the help. Things are worked out now

8. Originally Posted by qbkr21
Thanks Dan I appreciate the help. Things are worked out now
Always pleased to be of service!

-Dan