Which of the following functions is even?

Which of the following functions is even?

• A. f(x) = x^2
• B. f(x) = x
• C. f(x) = x^3
• D. f(x) = e^x

Answer: (A)

Even means the function is symmetric about the y-axis, so f(-x) = f(x) for all x. For f(x) = x^2, f(-x) = (-x)^2 = x^2, so it satisfies the condition and is even. For f(x) = x, f(-x) = -x, which is not equal to x, so not even. For f(x) = x^3, f(-x) = (-x)^3 = -x^3, not equal to x^3, so not even. For f(x) = e^x, f(-x) = e^{-x}, which is not e^x, so not even. Therefore, f(x) = x^2 is the only even function here.

Even means the function is symmetric about the y-axis, so f(-x) = f(x) for all x. For f(x) = x^2, f(-x) = (-x)^2 = x^2, so it satisfies the condition and is even. For f(x) = x, f(-x) = -x, which is not equal to x, so not even. For f(x) = x^3, f(-x) = (-x)^3 = -x^3, not equal to x^3, so not even. For f(x) = e^x, f(-x) = e^{-x}, which is not e^x, so not even. Therefore, f(x) = x^2 is the only even function here.