Question

Use the rational function to find the indicated function values. If a function value does not exist, state so.

x² - 4x-5
X-9
f(x) =
-; f(5), f(9), f(7)
...

Answer 1

rational function is:

f(x) = (x² - 4x - 5) / (x - 9)

To find f(5), we substitute x = 5:

f(5) = (5² - 4(5) - 5) / (5 - 9) = (-10) / (-4) = 5/2

To find f(9), we substitute x = 9:

f(9) = (9² - 4(9) - 5) / (9 - 9) = undefined

The function value f(9) is undefined because the denominator becomes zero, which makes the expression undefined.

To find f(7), we substitute x = 7:

f(7) = (7² - 4(7) - 5) / (7 - 9) = (-10) / (-2) = 5

Therefore, the function values are:

f(5) = 5/2

f(9) = undefined

f(7) = 5