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# Help

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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).

Feb 26, 2020

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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 $$q(-1)$$.

$$\begin{array}{|l|} \hline p(q(x)) = 4x+7,\\ \text{if q(x) = 2, then 4x+7 = 3, so 4x= 3-7 or 4x = -4 hence \mathbf{x=-1} } \\ \mathbf{q(-1)=2} \\ \hline \end{array}$$

Feb 26, 2020