Question

1a. If

Answer 1

The function f(g(x)) eventually simplifies to
   f(g(x) = (4/3)(x-5)(x-2)/(x² - 6x - 7)

a) The sum of the x-coordinates of the vertical asymptotes is the opposite of the x-coefficient in the denominator: 6.

b) Since the numerator and denominator are of the same degree, the horizontal asymptote is the overall multiplier: y = 4/3.


_____
Consider a quadratic with roots at "a" and "b". Then the factored form is
   (x-a)(x-b)
and the expanded form is
   (x² - (a+b)x + ab)
That is, the sum of the roots is the opposite of the x-coefficient. For this problem, that sum is the sum that is requested in part A.

Answer 2

Idk what the dollar signs or what the letters represent, would help but doesnt make sense