Question

A student claims that the function f(x)=x4+kx2+1 is an even function. Which statement best describes the student's claim?

Answer 1

Answer:

A

Step-by-step explanation:

Suppose x is odd. Then x^4 is also odd. So x^4 + 1 is even. Then for the whole function to be even, kx^2 should also be even. x^2 is obviously odd as x is odd. So to make kx^2 even, k should be even.

Now suppose x is even. Then x^4 + 1 is odd. So to make the function even, kx^2 should also be odd. But x is even, so kx^2 automatically becomes even, and then the whole function becomes odd. So the student's statement doesn't hold when x is even, no matter what the value of k is.

So the statement is true when x is odd and k is even.

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