Agraph of 2 functions is shown below. graph of function f of x equals negative 11 over 3 multiplied by x plus 11 over 3 and graph of function g of x equals x cubed plus 2 multiplied by x squared minus x minus 2 which of the following is a solution for f(x) = g(x)? x = −2 x = 1 x = 0 x = −1

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.

2

step-by-2step explanation: