The problem describes two functions, $H = C(m)$ and $m = a(s)$. $H = C(m)$ gives the speed of a car in mph after $m$ minutes. $m = a(s)$ converts $s$ seconds into $m$ minutes. The first part of the problem asks for the input and output of the composition $C(a(s))$. The second part of the problem introduces a function $f(v) = z$ that converts the speed $v$ in mph into $z$ the speed in ft/sec. The problem asks for the input and output of the function $f(C(m))$.

1. Problem Description

The problem describes two functions, $H = C(m)$ and $m = a(s)$. $H = C(m)$ gives the speed of a car in mph after $m$ minutes. $m = a(s)$ converts $s$ seconds into $m$ minutes. The first part of the problem asks for the input and output of the composition $C(a(s))$.

The second part of the problem introduces a function $f(v) = z$ that converts the speed $v$ in mph into $z$ the speed in ft/sec. The problem asks for the input and output of the function $f(C(m))$.

2. Solution Steps

First part: $C(a(s))$

* The input of $C(a(s))$ is $s$, which represents seconds.

* The function $a(s)$ converts $s$ seconds into $m$ minutes, so $a(s) = m$.

* The function $C(m)$ takes $m$ minutes as input and outputs $H$, which is the speed in mph.

* Therefore, the output of $C(a(s))$ is $H$, which represents the speed in mph.

Second part: $f(C(m))$

* The input of $f(C(m))$ is $m$, which represents minutes.

* The function $C(m)$ takes $m$ minutes as input and outputs $v=C(m)$, which is the speed in mph.

* The function $f(v)$ takes $v$ in mph and outputs $z$, the speed in ft/sec. Thus, $z = f(v) = f(C(m))$.

* Therefore, the output of $f(C(m))$ is $z$, which represents the speed in ft/sec.

3. Final Answer

For the composition $C(a(s))$:

Input: $s$ (seconds)

Output: $H$ (speed in mph)

For the function $f(C(m))$:

Input: $m$ (minutes)

Output: $z$ (speed in ft/sec)