Answer:
f(-x) = -4x^3 + 9x, f(x) is an odd function
Step-by-step explanation:
We are given that f(x) = 4x^3 - 9x. In order to solve this problem, we first need to understand what an odd function is and what an even function is. When we have an odd function, f(-x) = -f(x). Meaning, that if we plug -x in for x, we should get -f(x). On the other hand, with an even function, f(-x) = f(x). Even if you change the sign, when you simplify, you will get back the same function. In either case, we have to first find f(-x) to figure this problem out:
[tex]f(-x)=4(-x)^3-9(-x)\\f(-x)=-4x^3+9x[/tex]
We can see from our answer for f(-x) that it is equal to -f(x). We can verify this below:
[tex]-f(x)=-(4x^3-9x)\\-f(x)=-4x^3+9x[/tex]
Since f(-x) = -f(x), our function f(x) is an odd function
