Must the product of two even functions always be even?

Question

What about odd functions? (Must the product of two odd functions always be odd?) Why?

Answer 1

The only way you are going to get an odd answer is if you use an odd number function.

Functions describe mathematical paths and can be thought of as numbers; because they describe a specific set of numbers in space. So if you have only even numbers and you multiply them by only even numbers then you are going to only have even answers.

If you multiply any even number by any other even number then you will always get an even number that is a simple fact of math.

If you multiply an odd number by and odd number then you will end up with and odd number. So the functions that describe odd numbers are all odd numbers therefore the product will always be odd.

Remember that a function is a set of numbers, usually represented by a graph. If all those numbers are even then multiplying any of them will give you and even number. The same is true with odd functions. And when you multiply odd functions by even functions you end up with even functions because when you multiply odd numbers by even numbers you always end up with even numbers.

Answer 2

yes. but not for odds.

you must first understand that what an odd/even funciton is. an odd/even function is a function with terms where x is to an odd or even power.

given this, lets multiply 2 imaginary polynomials.
(a+b)(c+d) = ac+ad+bc+bd.
if the terms a,b,c,d all have an x to an even power, then when you multiply a and c, the x term MUST also be even. this holds true for all the other terms.

but this isnt tru for odds, since when you multiply 2 terms with different powers of the same base, you add the powers. 2 evens added up are even, but 2 odds added up are also even.

Answer 3

yes 2 even functions will be even and 2 odd functions will be even

Answer 4

yes the product of two even functions will be even

(2)(4)=8

the product of two odds will be even

(-2)(-4)=8

the product of an even and odd will be odd

(-2)(4)= -8

Answer 5

2 even numbers added together will always yield an even number. 2 even numbers multiplied together will always yield an even number. These rules are always true unless my grandson is doing the math, he's 3 yrs old.