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34 votes
34 votes
Suppose that the functions p and q are defined as follows.p(x) = -2x + 1q(x)=-x?Find the following.

Suppose that the functions p and q are defined as follows.p(x) = -2x + 1q(x)=-x?Find-example-1
User Bosko
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1 Answer

14 votes
14 votes

First let us find


(q\mathrm{}p)(x)
\begin{gathered} q(p(x))=q(-2x+1) \\ =-(-2x+1)^2 \\ So\text{ } \\ (q\mathrm{}p)(5)=-(-2*5+1)^2 \\ =-(9)^2 \\ =-81 \end{gathered}

Now let;s solve the second part


\begin{gathered} (p\mathrm{}q)(x)=p(q(x)) \\ =p(-x^2) \\ =-2(-x^2)+1 \\ =2x^2+1 \\ So\text{ (p.q)(5) will be } \\ (p\mathrm{}q)(5)=2(5)^2+1 \\ =51 \end{gathered}

User Shirry
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