Question

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

Answer 1

Choice A is correct.

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.

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.