Question

this is a multi - part item.
the average annual costs for owning two different refrigerators for x years is given by the two functions:
$f(x)=\frac{850 + 62x}{x}$ and $g(x)=\frac{1004 + 51x}{x}$
which of the following is true?
after one year, the cost of the refrigerator modeled by $g(x)$ is cheaper.
after one year, the costs are the same.
after one year, the cost of the refrigerator modeled by $f(x)$ is cheaper.

Explanation:

Step1: Substitute \( x = 1 \) into \( f(x) \)

Substitute \( x = 1 \) into \( f(x)=\frac{850 + 62x}{x} \). We get \( f(1)=\frac{850+62\times1}{1}=850 + 62=912 \).

Step2: Substitute \( x = 1 \) into \( g(x) \)

Substitute \( x = 1 \) into \( g(x)=\frac{1004+51x}{x} \). We get \( g(1)=\frac{1004 + 51\times1}{1}=1004+51 = 1055 \).

Step3: Compare \( f(1) \) and \( g(1) \)

Since \( 912<1055 \), after one year, the cost of the refrigerator modeled by \( f(x) \) is cheaper.

Answer:

After one year, the cost of the refrigerator modeled by \( f(x) \) is cheaper.