Advanced MathMediumSum of values of an odd function at symmetric inputs
Advanced Math practice question
The function f is defined by f(x) = x³ − x. What is the value of f(−2) + f(−1) + f(0) + f(1) + f(2)?
Answer: 0
f(−x) = −f(x), so f(−2) + f(2) = 0 and f(−1) + f(1) = 0, and f(0) = 0. The sum is 0. (Directly: −6 + 0 + 0 + 0 + 6 = 0.)
Common wrong answers
- If you answered 6
- 6 is f(2) alone.
- If you answered 12
- 12 adds |f(−2)| and |f(2)| without their signs.
- If you answered -6
- −6 is f(−2) alone.
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