Determine whether the function f(x) = -3x^3+4x is even, odd, or neither.
The definition of a odd function is f(-x)=-f(x) & the definition of an even function is f(-x)=f(x). All other cases are considered neither.
So lets test your function now. F(-x)= -3 (-x)^{3}+4(-x)= 3x^{3}-4x= -F(x). Therefore it is an odd function.
What does it mean??
This means if you check the input value for a odd function, lets say F(5), and has some value A. If you put in F(-5) you will get -A. So there is a symmetry about odd function. This is similar for even functions except you will find it would A again, so it has a different kind of symmetry.
So lets test your function now. F(-x)= -3 (-x)^{3}+4(-x)= 3x^{3}-4x= -F(x). Therefore it is an odd function.
What does it mean??
This means if you check the input value for a odd function, lets say F(5), and has some value A. If you put in F(-5) you will get -A. So there is a symmetry about odd function. This is similar for even functions except you will find it would A again, so it has a different kind of symmetry.