Answer
$C(x)=\dfrac{2\sqrt {100-p}}{25}+600$ $; 0\le p \le 100$
Work Step by Step
We will simplify the equation $p=-\dfrac{1}{4}x+100$ in order to isolate the $x$.
Thus, we have:
$p+\dfrac{1}{4}x=100\\\dfrac{1}{4}x=100-p$
or, $x=400-4p$
Therefore, the composite function will be:
$C(x)=\dfrac{\sqrt x}{25}+600 \\ =\dfrac{\sqrt {400-4p}}{25}+600 \\ =\dfrac{2\sqrt {100-p}}{25}+600$
We restrict the $p$ values to be less than $100$ to avoid a negative in the root:
Domain: $0\le p \le 100$
