Refer to the functions $r$ and $p$. Find the function $(r-p)(x)$ and write the domain in interval notation.
\[
r(x)=6 x
\]
\[
p(x)=x^{2}-2 x
\]
\[
q(x)=\sqrt{8-x}
\]
Part: $0 / 2$
Part 1 of 2
\[
(r-p)(x)=
\]

Step 1 ：Given the functions \(r(x)=6x\) and \(p(x)=x^{2}-2x\), we are asked to find the function \((r-p)(x)\) and write the domain in interval notation.

Step 2 ：To find the function \((r-p)(x)\), we need to subtract the function \(p(x)\) from \(r(x)\). This means we will subtract each term of \(p(x)\) from \(r(x)\).

Step 3 ：Subtracting \(p(x)\) from \(r(x)\) gives us the function \((r-p)(x) = x*(8 - x)\).

Step 4 ：The domain of a function is the set of all possible input values (often the 'x' variable), which produce a valid output from a particular function. For this function, the domain is all real numbers because there are no restrictions on the input values.

Step 5 ：Thus, the domain of the function \((r-p)(x)\) is \((-∞, ∞)\).

Step 6 ：Final Answer: The function \((r-p)(x)\) is \(x*(8 - x)\) and its domain in interval notation is \(\boxed{(-\infty, \infty)}\).