Answer:
c = 3
Step-by-step explanation:
We want to know if the is a value, c, such that f(c) = 6.
Set the equation equal to 6 and solve for x:
6 = (x^2 - 5x - 24)/(x-8)
Note that we can factor the top equation:
(x^2 - 5x - 24) = (x -8)(x+3) [I deliberately looked for (x-8) as one of the factors, since it would cancel with the numerator.]
That leads to:
6 = [(x -8)(x+3)]/(x-8)
6 = (x+3)
x = 3
that means c = 3, since f(3) = 6.
