Question

Is f(x)=x to the 4th power - x to the 2nd power an even function

Answer 1

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Answer 2

Yes. f(x) = x⁴ - x² is an even function

Step-by-step 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