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Determine whether f is even, odd, or neither?

by akt223
Tags: determine
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akt223
#1
Jan3-05, 03:52 PM
P: 2
I've tried looking through my book to see how to do these, but I just can't find it. Any help would be appreciated:

1) f(x) = 2x^5 - 3x^2 +2

2) f(x) = x^3 - x^7

3) f(x) = (1-x^2)/(1+x^2)

4) f(x) = 1/(x+2)

Thanks in advance!
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Dr Transport
#2
Jan3-05, 03:55 PM
Sci Advisor
PF Gold
P: 1,469
the definition of an even and an odd function is as follows:

[tex] f(-x) = f(x) [/tex] is and even function and

[tex] f(-x) = -f(x) [/tex] is an odd function.
akt223
#3
Jan3-05, 04:01 PM
P: 2
Alright, I think I get it, thanks.

HallsofIvy
#4
Jan3-05, 05:05 PM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,339
Determine whether f is even, odd, or neither?

It is also true (easy to prove) that a rational function (polynomial or quotient of polynomials) is even if and only if all exponents of x are even, odd if and only if all exponents of x are odd.

Of course, functions don't always have "exponents"! sin(x) is an odd function and cos(x) is an even function.
rachmaninoff
#5
Jan3-05, 05:19 PM
P: n/a
Of course, functions don't always have "exponents"! sin(x) is an odd function and cos(x) is an even function.
But the series expansions precisely consist of only odd-numbered and only even-numbered polynomial terms, respectively. It's quite elegant.


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