Question

Which statement best describes how to determine wether f(x)=x^3 +5x+1 is an even function

Answer 1

Answer: second option.

Step-by-step explanation:

By definition, a function is even when:

$f(x) = f(-x)$

Then, knowing this, given the function $f(x)=x^3 +5x+1$ you can substitute $-x$ into this function:

$f(-x)=(-x)^3 +5(-x)+1$

Now you need to simplify the function. Then you get:

 $f(-x)=-x^3 -5x+1$

In this case, you can see that:

 $f(x)\neq f(-x)$

Therefore, the function $f(x)=x^3 +5x+1$ is not even.

As you observed in the procedure above, the statement that best describes how to determine whether the given function is even is:

Determine is $(-x)^3 +5(-x)+1$ is equivalent to $x^3 +5x+1$