Question

The function ƒ is given by fx=x3+x . Which of the following statements is true and supports the claim that f is an odd function and not an even function?

a) f(0)=-f(0)
b) -f(3)=f(3)
c) f(-3)=f (3)
d) f(-3) =-f(3)

Answer 1

f(x) = x^3 + x is an odd function because f(-x) = -f(x), supporting statement d) f(-3) = -f(3).

Step-by-step explanation:

An odd function satisfies the condition y(x) = -y(-x) for all x values in the domain. In this case, we need to determine if the function f(x) = x^3 + x is odd or even.

To check if it is odd, we substitute -x for x and simplify: f(-x) = (-x)^3 + (-x) = -x^3 - x.

Now, we compare f(-x) to -f(x): -f(x) = -(x^3 + x) = -x^3 - x.

Since f(-x) = -f(x), we can conclude that f(x) is an odd function. Therefore, the correct statement is d) f(-3) = -f(3).