Chapter 3.4, Problem 44E

(a)

To determine

To sketch:The graph of the function $C\left(x\right)$ .

Answer to Problem 44E

The graph of the function is shown in figure (1).

Explanation of Solution

The given function is a greatest integer function.

The graph of the function is shown below.

  

Figure (1)

Therefore, the graph of the function is shown in figure (1).

(b)

To determine

To find: The domain and range of the function.

Answer to Problem 44E

The domain of the function is $x\ge 0$ and the range of the function is $y\ge 0$ .

Explanation of Solution

Consider figure (1),

The domain of the function is,

  $x\ge 0$

The range of the function is,

  $y\ge 0$ .

Therefore, the domain of the function is $x\ge 0$ and the range of the function is $y\ge 0$ .

(c)

To determine

To sketch: The graph of $C^{-1}\left(x\right)$

Answer to Problem 44E

The graph of $C^{-1}\left(x\right)$ is shown in Figure (2).

Explanation of Solution

The graph of $C^{-1}\left(x\right)$ is shown below.

  

Figure (2)

Therefore, the graph of the inverse function is shown in figure (2).

(d)

To determine

To find: The domain and range of the inverse function.

Answer to Problem 44E

The domain of the inverse function is $x\ge 0$ and the range of the inverse function is $y\ge 0$ .

Explanation of Solution

Consider figure (2),

The domain of the function is,

  $x\ge 0$

The range of the function is,

  $y\ge 0$ .

Therefore, the domain of the function is $x\ge 0$ and the range of the function is $y\ge 0$ .

(e)

To determine

To find: The real world situation modelled by $C^{-1}\left(x\right)$ .

Answer to Problem 44E

The real world situation modelled by $C^{-1}\left(x\right)$ is stated below.

Explanation of Solution

The real world situation modelled by $C^{-1}\left(x\right)$ is the flying of an aeroplane.