Answer:
Domain: (-infinity, -4)∩(-4, 4)∩(4, infinity); range: (-infinity, 0)∩(0, infinity)
Step-by-step explanation:
In f(x)=3x-12/x^2-16, please use parentheses around the denominator x^2 - 16, so that there's no ambiguity in regard to your dividing by x^2 or by (x^2 - 16). Thanks. Then we have:
f(x)=3x-12 / (x^2-16)
This can be factored, as follows:
f(x) = 3(x-4) / [(x-4)(x+4)]. Note that x can equal neither 4 nor -4, due to the resultant division by zero.
We can cancel the x-4 terms, obtaining f(x) = 3/(x+4), remembering that x can still not equal 4 or -4.
Then the domain is "the set of all real numbers other than 4 and -4," and the domain is "the set of all real numbers other than zero."