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Q. Let a function $f$ satisfying the relation $f(x+8)=f(x)$ and $f(x)=\begin{cases}x^2, & 0 \leq x \leq 2 \\ (4-x)^2, & 2< x \leq 4 \\ 2(x-4), & 4< x< 6 \\ -2(x-8), & 6 \leq x \leq 8\end{cases}$.
The value of $f(19) + f(63)+f(99) + f(-73)$ is equal to

Relations and Functions - Part 2

Solution:

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$f(3) + f(7) + f(3) + f(7)$
$= 2 [f(3) + f(7)]$
$= 2 [1 + 2] = 6.$