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Find (p@q)(x) and (q@p)(x) {:[p(x)=x^(2)],[q(x)=x+3]:} Write your answer as a polynomial in simplest form. {:[(p@q)(x)=◻],[(q@p)(x)=◻]:}

Find (p∘q)(x) (p \circ q)(x) and (q∘p)(x) (q \circ p)(x) \newlinep(x)=x2q(x)=x+3 \begin{array}{l} p(x)=x^{2} \\ q(x)=x+3 \end{array} \newlineWrite your answer as a polynomial in simplest form.\newline(p∘q)(x)=□(q∘p)(x)=□ \begin{array}{l} (p \circ q)(x)=\square \\ (q \circ p)(x)=\square \end{array}

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Q. Find (p∘q)(x) (p \circ q)(x) and (q∘p)(x) (q \circ p)(x) \newlinep(x)=x2q(x)=x+3 \begin{array}{l} p(x)=x^{2} \\ q(x)=x+3 \end{array} \newlineWrite your answer as a polynomial in simplest form.\newline(p∘q)(x)=□(q∘p)(x)=□ \begin{array}{l} (p \circ q)(x)=\square \\ (q \circ p)(x)=\square \end{array}
  1. Find p@q(x)p@q(x): Find (p@q)(x)(p@q)(x)\newlinep(x)=x2p(x) = x^2\newlineq(x)=x+3q(x) = x + 3\newline(p@q)(x)(p@q)(x) means p(q(x))p(q(x))\newlineSo, p(q(x))=p(x+3)p(q(x)) = p(x + 3)
  2. Substitute q(x)q(x) into p(x)p(x): Substitute q(x)q(x) into p(x)p(x) p(x+3)=(x+3)2p(x + 3) = (x + 3)^2
  3. Expand (x+3)2(x + 3)^2: Expand (x+3)2(x + 3)^2 (x+3)2=x2+6x+9(x + 3)^2 = x^2 + 6x + 9 So, (p@q)(x)=x2+6x+9(p@q)(x) = x^2 + 6x + 9
  4. Find q@p(x) q@p(x) : Find (q@p)(x) (q@p)(x) p(x)=x2 p(x) = x^2 q(x)=x+3 q(x) = x + 3 (q@p)(x) (q@p)(x) means q(p(x)) q(p(x)) So, q(p(x))=q(x2) q(p(x)) = q(x^2)
  5. Substitute p(x)p(x) into q(x)q(x): Substitute p(x)p(x) into q(x)q(x) q(x2)=x2+3q(x^2) = x^2 + 3 So, (q@p)(x)=x2+3(q@p)(x) = x^2 + 3

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