Question

p(x) = – 2xq(x)=x^2-1(qop)(4)(poq)(4)

Answer 1

Let's begin by identifying key information given to us:

$\begin{gathered} p\mleft(x\mright)=-2x \\ q\mleft(x\mright)=x^2-1 \end{gathered}$

We are to calculate for their composite form as shown below:

$\begin{gathered} \mleft(qop\mright)\mleft(4\mright)=p(q\mleft(4\mright)) \\ \Rightarrow q(-2x) \\ \Rightarrow{\mleft(-2x\mright)}^2-1=4x^2-1 \\ 4x^2-1 \\ x=4 \\ 4(4^2)-1=4(16)-1=64-1=63 \\ \therefore(qop)(4)=63 \end{gathered}$

$\begin{gathered} (poq)\mleft(4\mright)=p\mleft(q\mleft(4\mright)\mright) \\ \Rightarrow p\mleft(x^2-1\mright) \\ \Rightarrow-2\mleft(x^2-1\mright)=-2x^2+2 \\ -2x^2+2 \\ x=4 \\ \Rightarrow-2(4^2)+2=-2(16)+2=-32+2=-30 \\ \therefore(poq)(4)=-30 \end{gathered}$