even odd functions

**qbkr21** · January 9th 2007, 12:37 PM

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

**topsquark** · January 9th 2007, 01:10 PM

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

**qbkr21** · January 9th 2007, 01:13 PM

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

**topsquark** · January 9th 2007, 01:22 PM

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

**qbkr21** · January 9th 2007, 01:29 PM

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.

**topsquark** · January 9th 2007, 01:33 PM

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

**qbkr21** · January 9th 2007, 01:34 PM

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

**topsquark** · January 9th 2007, 01:48 PM

Originally Posted by qbkr21

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

Always pleased to be of service!

-Dan

Thread: even odd functions

LinkBack

Thread Tools

Display

even odd functions

Similar Math Help Forum Discussions

Match the functions with their contour plots labeled A - D. Most of these functions a

Circular functions as opposed to traditionally determined trigonometric functions?

[SOLVED] Integration of Incomplete Beta Functions and Hypergeometric Functions

[SOLVED] Chain rule with functions depending on other functions

ntegration of Functions that are the Derivatives of Analytic Functions

Search Tags