Answer:
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