g(x) = (x+3)/(x^{2}4)
The domain refers to all of the x values that the function can take on. In a rational expression like the one above, we have to be careful that the denominator is never 0, since division by 0 is undefined. We can factor the denominator of g(x) as follows:
g(x) = (x+3)/((x+2)(x2)
The denominator will be zero when x = 2 or 2. Otherwise, g(x) is defined on all other values of x. So the domain of g(x) is "x = all x not equal to 2 or 2". In interval notation, the domain is:
(∞,2)U(2,2)U(2,+∞)
On a number line, draw it as follows:
∞ <======o=====o=======> +∞
2 2
3/29/2014

Philip P.
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