Final answer:
To evaluate the rational function g(x) at x=7, substitute 7 into the function, then compute the numerator and denominator separately and divide them to find g(7) is -16/9.
Step-by-step explanation:
The student's question involves evaluating a rational function by substituting a given value for the variable x. To find g(7), we need to substitute x = 7 into the rational function g(x) = (x²-4x-5)/(x²-6x-16) and then simplify.
First, we calculate the numerator and the denominator separately:
- Numerator: (7² - 4(7) - 5) = (49 - 28 - 5) = 16
- Denominator: (7² - 6(7) - 16) = (49 - 42 - 16) = -9
Now, we divide the numerator by the denominator to get the value of g(7):
g(7) = 16 / (-9) = -16/9
Therefore, g(7) is -16/9.