Question

Which statement best describes how to determine whether f(x) = x^A - x^2 is an even function?

a) Determine whether (-x)^A – (-x)^2 is equivalent to A - x.
b) Determine whether (x^2) – (-x) is equivalent to A + x.
c) Determine whether (-x)^4 – (-x)^2 is equivalent to -(x - x).
d) Determine whether (A) – (-x^2) is equivalent to -(x + x^2).

Answer 1

To determine whether the function f(x) = x^A - x^2 is an even function, we need to check if it satisfies the condition f(x) = f(-x), which means that the function is symmetric with respect to the y-axis.

Step-by-step explanation:

To determine whether the function f(x) = x^A - x^2 is an even function, we need to check if it satisfies the condition f(x) = f(-x), which means that the function is symmetric with respect to the y-axis.

Let's substitute -x for x in the function and simplify:

f(-x) = (-x)^A - (-x)^2 = (-1)^A * x^A - (-1)^2 * x^2 = x^A - x^2 = f(x)

Since f(-x) = f(x), we can conclude that the function is indeed an even function.