ANSWER
Yes. f(x) = x⁴ - x² is an even function
EXPLANATION
A function is even if f(x) = f(-x) (symmetrical about the y-axis).
We see that
f(-x) = (-x)⁴ - (-x)²
Note that
(-x)⁴ = (-1·x)⁴ = (-1)⁴·(x)⁴ = x⁴
and the same follows for (-x)²; therefore
f(-x) = (-x)⁴ - (-x)²
= (x)⁴ - (x)²
= f(x)
so it is an even function
[tex] f(x)=x^4-x^2\\
f(-x)=(-x)^4-(-x)^2=x^4-x^2\\\\
f(x)=f(-x) \Rightarrow \text{is even} [/tex]
