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The function g is defined below. g(x)=x+3/(x^2-4) Find all values of that are NOT in the domain of g.

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1 Answer

g(x) = (x+3)/(x2-4)
 
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)(x-2)
 
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

Comments

High Philip:
 
[ sign of equality should never appear before ∝ , no quantity ever becomes equal infinity.
Right your are.  Corrected.  Thx.

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