Question

Evaluate the indicated function for f(x) = x² − 1 and g(x) = x − 10 algebraically. If possible, use a graphing utility to verify your answer. (f/g)(0)

a) f/g(0) = (0² - 1)/(0 - 10)

b) f/g(0) = (0 - 10)/(0² - 1)

c) f/g(0) = (0² - 1)/(0 + 10)

d) f/g(0) = (0 + 10)/(0² - 1)

Answer 1

The correct evaluation of the function (f/g)(0) for f(x) = x² - 1 and g(x) = x - 10 is a) f/g(0) = (0² - 1)/(0 - 10), which equals 0.1.

Step-by-step explanation:

To evaluate the function (f/g)(0) for f(x) = x² − 1 and g(x) = x − 10, we will plug in x = 0 into both functions and then divide the output of f(x) by the output of g(x). Given the choices, the correct way to do this is:

f/g(0) = (0² - 1)/(0 - 10)

Now let's calculate it step by step:

1. First, we evaluate f at x = 0, which gives us f(0) = 0² − 1 = − 1.
2. Next, we evaluate g at x = 0, which gives us g(0) = 0 − 10 = − 10.
3. To find the value of (f/g)(0), we divide f(0) by g(0), resulting in − 1 / − 10. This simplifies to 1/10 or 0.1.

The correct choice is a) f/g(0) = (0² - 1)/(0 - 10), and the value is 0.1.