Answer:
x = 1
Step-by-step explanation:
The graphs of the functions intersect at x = 1.
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There are a number of ways you can determine that x=1 is the only viable answer choice.
Factoring f(x), you get
f(x) = (11/3)(1 -x)
This will only have integer values for values of x of the form 3n+1. The only answer choices of that form are x=-2 and x=1. Each of these is easy enough to try in the two functions:
f(-2) = 11, g(-2) = 0 . . . . f(-2) ≠ g(-2), so -2 is not a solution
f(1) = 0, g(1) = 0 . . . . . . .f(1) = g(1), so 1 is a solution
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You can subtract one function from the other and search for zeros of the composition
(g-f)(x) = x^3 +2x^2 +8/3x -17/3
Descartes' rule of signs tells you this has one positive real solution and 0 or 2 negative real solutions. x=1 is the only positive real answer choice. It also happens to be the only real solution of this cubic.
