That is not the correct concept to used to determine if a function is even or odd. Do you know the definition for even and odd functions?
a) f(x) is an even function if f(x)=f(-x)
b) f(x) is an odd function if f(x)=-f(-x)
c) any function f(x) can be written as where is the 'even part of f(*)' and is the 'odd part of f(*)'
d) for any function f(x) is...
e) given f(x), one computes with (1) its even and odd part. If then f(*) is an even function. If , then f(*) is an odd function. If and , then f(*) in neither even nor odd...
If you have a polynomial with only even exponents (a constant "c" can be written as c*x^0, and zero is even, so constant terms are even...), then the function P(x) is even.
If you have a polynomial with only odd exponents, then the function P(x) is odd.
In your examples, there is an absolute value term, which is not polynomial.
I just took a quiz and got this question wrong:
Is the given functions even, odd, or neither? .
I answered it was odd because the of both terms have a power of 1:
Why did I get this answer wrong?
That rule about "all odd exponents" or "all even exponents"
. . works with polynomials only. .(Edit: as TheChaz already pointed out.)
If is "inside" another function, all bets are off!
Look at that function again: .
If is negative ,
. . we have: . +
@Soroban, cheme, TheChaz
Thanks! I was wondering why it worked when my instructor used this method to determine if a function was even or odd. Now I know the using the powers of exponents to determine if a function is even or odd, only works when you have polynomials only.
I was trying to understand general rule c, and d. May you solve a problem using rule c and d.
... so that...
Because neither nor is 'identically 0' , then f(x) is 'neither even nor odd'...
If You will use this approach in the future, You will be 'very lucky' because it works for any type of fucntion, not only for polynomials...