Thanks. I just could not have seen this so easily. Now I got it.A function is odd if f(-x) = -f(x) and even if f(-x) = f(x). So what do you think of sin(x^3)? Or did you mean (sin(x))^3?
It's interesting. If someone had asked me if a composition of two odd functions is odd or even I might have guessed even. But, if ##f## and ##g## are both odd, then:Thanks. I just could not have seen this so easily. Now I got it.
##f\circ g## is even regardless of whether ##f## is even, odd, or neither.It's interesting. If someone had asked me if a composition of two odd functions is odd or even I might have guessed even. But, if ##f## and ##g## are both odd, then:
##f(g(-x)) = f(-g(x)) = - f(g(x))##
Hence ##f \circ g## is odd. I guess it's like multiplying two odd numbers.
Also, what if we have an odd function and an even function. E.g. if ##g## is even and ##f## is odd:
##f(g(-x)) = f(g(x))##
Hence ##f \circ g## is even.
And, it's the same if you have any number of odd functions and one even function. A single even function kills all the oddness! The same as multiplication.
A function is odd if f(-x) = -f(x) and even if f(-x) = f(x).
Why is that? phyzguy is just using the definitions of odd and even, the first things you should be looking for.I just could not have seen this so easily.
Because I focused on graph or geometry to recognize them.Why is that? phyzguy is just using the definitions of odd and even, the first things you should be looking for.
But you should also keep the definition in mind...Because I focused on graph or geometry to recognize them.