Question

The function given by \( f(x) = |x|^3 \) is

• A. even
• B. odd
• C. neither
• D. both

Hint:

For functions involving absolute value, test symmetry about the y-axis: \( f(-x) = f(x) \) implies even.

Answer 1

The Correct Option is A

We are given: \[ f(x) = |x|^3 \] Now test whether it's even or odd.
Step 1: Compute \( f(-x) \): \[ f(-x) = |-x|^3 = |x|^3 = f(x) \] So, \( f(-x) = f(x) \text{function is even} \) Also check: \[ f(-x) = -f(x)? |x|^3 \neq -|x|^3 \text{not odd} \] Therefore, \[ \boxed{\text{Even}} \]