Question

If functions f and g are both even functions, is the product fg even? If functions f and g are both odd functions, is the product fg odd? What if f is even and g is odd? Justify your answers in written sentences.

Answer 1

@zzr0ck3r

Answer 2

\[x^3*x^3 = x^{3+3}=x^6=(x^3)^2\]

Answer 3

the product of even functions is EVEN
the product of odd functions is EVEN

Answer 4

what is f is even and g is odd @zzr0ck3r

Answer 5

The only function whose domain is all real numbers which is both even and odd is the constant function which is identically zero (i.e., f(x) = 0 for all x).[1]
The sum of two even functions is even, and any constant multiple of an even function is even.
The sum of two odd functions is odd, and any constant multiple of an odd function is odd.
The difference between two odd functions is odd.
The difference between two even functions is even.
The product of two even functions is an even function.
The product of two odd functions is an even function.
The product of an even function and an odd function is an odd function.
The quotient of two even functions is an even function.
The quotient of two odd functions is an even function.
The quotient of an even function and an odd function is an odd function.
The derivative of an even function is odd.
The derivative of an odd function is even.
The composition of two even functions is even, and the composition of two odd functions is odd.
The composition of an even function and an odd function is even.
The composition of any function with an even function is even (but not vice versa).
The integral of an odd function from −A to +A is zero (where A is finite, and the function has no vertical asymptotes between −A and A).
The integral of an even function from −A to +A is twice the integral from 0 to +A (where A is finite, and the function has no vertical asymptotes between −A and A. This also holds true when A is infinite, but only if the integral converges).

Answer 6

this is on wiki btw

Answer 7

thanks