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2 problems match “symmetry of functions”. Clear

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1. Value of f(3) from symmetry conditions ●●○○○ 20 ptsLet $f(x)$ be a function with domain $\mathbb{R}$ such that $f(x+1) = f(-x-1)$ and $f(2-x) = -f(x)$ for all real $x$. Find the value of $f(3)$.
2. Distinct values of a symmetric function ●●●●○ 100 ptsGiven a function $f$ for which $f(x) = f(398 - x) = f(2158 - x) = f(3214 - x)$ for all real $x$, what is the largest number of different values that can appear in the list $f(0), f(1), f(2), \ldots, f(999)$?