Find the domain and range of f(x)=3x-12/x^2-16

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."

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