Question

Determine if the function is an even function, an odd function or neither.

Answer 1

Answer:

Choice A is correct.

Step-by-step explanation:

We have  given a function.

y = 2x⁴ +2x²

suppose y = f(x) , we get,

f(x) =  2x⁴ +2x²

We have to find that is this function is even or  odd?

A function is even if f(x) = f( -x).

A function is odd if f(x) = - f(x).

Putting x = -x in f(x) we get,

f(-x) = 2(-x)⁴+2(-x)²

f(-x)  = 2x⁴+2x²

f(-x) = f(x)

So, the function is even.

Answer 2

Answer: Option a.

Step-by-step explanation:

By definition, a functioon is even when:

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

And it is odd when:

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

Therefore, you can verify if the function is even substituting -x into the function:

$f(-x)=2(-x)^{4}+2(-x)^{2}\\f(-x)=2x^{4}+2x^{2}$

Then:

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

It is an even function.