Question

refer to the functions r, p, and q. find the function (p·q)(x) and write the domain in interval notation.\\( r(x)=7x \\)\\( p(x)=x^2 + 5x \\)\\( q(x)=sqrt{9 - x} \\)\\( \text{part: } 0 / 2 \\)\\( \text{part 1 of 2} \\)\\( (p·q)(x)=\square \\)

Explanation:

Step1: Recall the product of functions

The product of two functions \( (p \cdot q)(x) \) is defined as \( p(x) \cdot q(x) \).
We know \( p(x)=x^{2}+5x \) and \( q(x)=\sqrt{9 - x} \), so we multiply these two functions.
\[
(p\cdot q)(x)=p(x)\cdot q(x)=(x^{2}+5x)\cdot\sqrt{9 - x}
\]
We can factor out an \( x \) from the first polynomial:
\[
(p\cdot q)(x)=x(x + 5)\sqrt{9 - x}
\]

Answer:

\(x(x + 5)\sqrt{9 - x}\) (or \((x^{2}+5x)\sqrt{9 - x}\))