Suppose $f(x),g(x),h(x)$ are all linear functions, and $j(x)$ and $k(x)$ are defined by$$j(x) = \max\{f(x),g(x),h(x)\},$$$$k(x) = \min\{f(x),g(x),h(x)\}.$$This means that, for each $x$, we define $j(x)$ to be equal to either $f(x),$ $g(x),$ or $h(x),$ whichever
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