if (p(x)=2x^{2}-4x) and (q(x)=x - 3), what is ((pcirc q)(x))?\n(2x^{2}-4x + 12)\n(2x^{2}-16x +…

Explanation:

Step1: Recall composition formula

$(p\circ q)(x)=p(q(x))$

Step2: Substitute $q(x)$ into $p(x)$

Since $q(x)=x - 3$, then $p(q(x))=2(q(x))^{2}-4(q(x))=2(x - 3)^{2}-4(x - 3)$

Step3: Expand $(x - 3)^{2}$

Using $(a - b)^{2}=a^{2}-2ab + b^{2}$, where $a=x$ and $b = 3$, we have $(x - 3)^{2}=x^{2}-6x + 9$. So $2(x - 3)^{2}=2(x^{2}-6x + 9)=2x^{2}-12x+18$

Step4: Expand $-4(x - 3)$

$-4(x - 3)=-4x+12$

Step5: Combine like - terms

$2x^{2}-12x + 18-4x+12=2x^{2}+(-12x-4x)+(18 + 12)=2x^{2}-16x+30$

Answer:

$2x^{2}-16x + 30$