Final answer:
To find the values of x that are not in the domain of the function, we need to find the values of x that make the denominator equal to zero. We set the denominator equal to zero and solve for x. The values of x that are not in the domain of the function are -6 and 2.
Step-by-step explanation:
The function f is defined as g(x) = (x²-4x+3)/(x²+4x-12). To find the values of x that are not in the domain of f, we need to find the values of x that make the denominator of g(x) equal to zero, because division by zero is undefined. So, we set the denominator equal to zero and solve for x: (x²+4x-12) = 0. This is a quadratic equation, which can be factored or solved using the quadratic formula.
To factor the equation, we look for two numbers that multiply to -12 and add to 4. Those numbers are 6 and -2. So, we can rewrite the equation as (x+6)(x-2) = 0. Setting each factor equal to zero, we get x+6=0 and x-2=0. Solving for x, we find that x=-6 and x=2. Therefore, the values of x that are not in the domain of f are -6 and 2.