Which of the following functions is an even function, satisfying f(-x) = f(x) for all x in its domain?
Answer and explanation
Correct answer: D. f(x) = x^4 + 3x^2 - 5
- Step 1: An even function satisfies f(-x) = f(x).
- Step 2: For f(x) = x^4 + 3x^2 - 5: f(-x) = (-x)^4 + 3(-x)^2 - 5 = x^4 + 3x^2 - 5 = f(x). Thus it is even.
Answer
f(x) = x^4 + 3x^2 - 5.
Why not the others: Option f(x) = x^3 - 4x is an odd function because f(-x) = -f(x). Option f(x) = sin(x) is an odd function. Option f(x) = x^5 + 2x^2 is neither even nor odd.
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