Question

A student claims that the function f(x)=x^4 + kx^2 + 1 is an even function. Which statement best describes the student's claim?

The student's claim is true for all values of k.
The student's claim is only true for even values of k.
The student's claim is not true for any value of k.
The student's claim is only true for odd values of k.

I think the answer is the third one or fourth one but I am not sure because I substituted "x" with 1 and -1 into the equation and got the answers:
(1)= 2k
(-1)= k

Answer 1

A function is even if f(a) = f(-a)

let's test it

f(a) = a^4 + ka^2 + 1
f(-a) = (-a)^4 + k(-a)^2 + 1 = a^4 + ka^2 + 1

so, what do you think?

Answer 2

That they are correct, this is an even function ?