Refer to the functions $r$ and $p$. Find the function $(r-p)(x)$ and write the domain in interval notation.
$$r(x)=6x$$
$$p(x)=x^2-2x$$
$$q(x)=\sqrt{8-x}$$
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 $(r-p)(x)=x\ast (8-x)$.

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 $(-\infty ,\infty )$.

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