Chapter 3.4, Problem 19Q

Solution

Find $C(g(d))$ and $C(g(400))$ . What does $C(g(400))$ represents?

  $C(g(d))=0.043d$

  $C(g(400))=17.2$

  $C(g(400))$ Represents the cost of gasoline used by car to travel 400 miles distance.

Given:

The cost (in dollars) of g gallons of gasoline can be modeled by $C(g)=2.15g$ . The amount of gasoline used by a car can be modeled by $g(d)=0.02d$ where d is the distance (in miles) that the car has been driven.

Concept Used:

• The composition function $f\circ g$ can be found by replacing x by $g\left(x\right)$ in the function $f\left(x\right)$
• The domain of a function $y=f\left(x\right)$ is the set of all x values for which the function is defined.
• A rational function $y=f\left(x\right)$ is undefined for the values of x , for which the denominator is zero.
• A radical function is defined for positive values greater than or equal to zero.
• Zero product property: if $a\cdot b=0\text{then}a=0\text{or}b=0$

Calculation:

The cost (in dollars) of g gallons of gasoline can be modeled by $C(g)=2.15g$

The amount of gasoline used by a car can be modeled by $g(d)=0.02d$

  $\begin{array}{c}C(g(d))=c(0.02d)\\ =2.15(0.02d)\\ =0.043d\end{array}$

  $\begin{array}{c}C(g(400))=c(0.02(400))\\ =c(8)\\ =2.15(8)\\ =17.2\end{array}$

  $C(g(400))$ Represents the cost of gasoline used by car to travel 400 miles distance.