Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 1.7 Junior Find the answer

Let the function $f(x) = x^2 \sin x + 2$ . If $f(a) = 15$ , then $f(-a) = \boxed{-11}$ .

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

Given that $f(a) + f(-a) = 4$ , therefore $f(-a) = 4 - 15 = -11$ .

Hence, the answer is $\boxed{-11}$ .

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.