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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 $q(-1)$.

 Jul 31, 2023
 #1
avatar+757 
+1

I'm guessing the answer to this question. If we plug in q(-1) into p(q(x)) = 4x+7, we can see that p(q(-1)) = 3. The problem tells us the p(2) is equal to 3. Through this, we can tell that q(-1) is equal to 2. 

 Jul 31, 2023
 #2
avatar+183 
-2

The assumption in this answer is that \(p(x)\) is injective in other words \(p(x)=p(a) \implies x=a\). Since \(p(x)\) is linear, it is injective so this solution works.

plaintainmountain  Aug 1, 2023

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