Answer
$C(x)=\dfrac{\sqrt {1000-5p}}{10}+400$; $0\le p\le 200$
Work Step by Step
We will simplify the equation $p=-\dfrac{1}{5}x+200$ in order to isolate the $x$.
Thus, we have:
$p+\dfrac{1}{5}x=200$
or, $x=1000-5p$
Therefore, the composite function will be:
$C(x)=\dfrac{\sqrt x}{10}+400 \\ =\dfrac{\sqrt {1000-5p}}{10}+400$
We restrict $p$ to be less than or equal to $200$ to avoid a negative in the root:
Domain: $0\le p\le 200$
