Register to reply

Determine whether f is even, odd, or neither?

by akt223
Tags: determine
Share this thread:
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!
Phys.Org News Partner Mathematics news on Phys.org
Researcher figures out how sharks manage to act like math geniuses
Math journal puts Rauzy fractcal image on the cover
Heat distributions help researchers to understand curved space
Dr Transport
#2
Jan3-05, 03:55 PM
Sci Advisor
PF Gold
P: 1,481
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: 39,682
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.


Register to reply

Related Discussions
Determine the frequencies Mechanical Engineering 0
Determine R value... Classical Physics 12
Determine M(x) Calculus & Beyond Homework 14
Determine if G and H are isomorphic Precalculus Mathematics Homework 8
KCL / KVL to determine Vo Introductory Physics Homework 2