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Mathematics
General Math
Which procedure takes the minimum time to solve modulus functions?
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[QUOTE="I like Serena, post: 6785250, member: 312166"] Let's pick your $|x-5|+|x-2|=9$. We define the function $f(x) = |x-5|+|x-2|-9$. So we want to know for which values of $x$ we have that $f(x)=0$. Critical points are $x=2$ and $x=5$ for which we have $f(2)=-6$ and $f(5)=-6$. Let's pick $x=0$ and $x=6$ as they are below respectively above the critical points. Those have $f(0)=-2$ and $f(6)=-4$. From those we can deduce that the graph looks like this: [ATTACH type="full"]312023._xfImport[/ATTACH] That is, the critical points are on the same side of the x-axis, so there cannot be a zero in between. Below $x=2$ the graph slopes towards the x-axis, so there must be a zero there. Above $x=5$ the graph slopes towards the x-axis as well, so there must be a zero there as well. For values below $x=2$ all signs are negative, so we need to solve $-(x-5)+-(x-2)-9=0 \implies -2x-2=0 \implies x=-1$. For values above $x=5$ all signs are positive, so we need to solve $+(x-5)++(x-2)-9=0 \implies 2x-16=0 \implies x=8$. Therefore the solutions are $x=-1$ and $x=8$. [/QUOTE]
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Forums
Mathematics
General Math
Which procedure takes the minimum time to solve modulus functions?
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