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you have linear functions p(x) and q(x).  You know p(2)=3, and p(q(x))=4x+7 for all x.  Find q(-1).

 Mar 30, 2019
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\(p(q(-1))=4(-1)+7 = 3\\ \text{linear functions are a bijection, i.e. }\\ p(x)=a \text{ and } p(y)=a \Rightarrow x = y\\ p(2)=3 \text{ and } p(q(-1))=3 \Rightarrow q(-1)=2\)

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 Mar 30, 2019

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