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.

Question

g(x)=x+3/(x^2-4) 

x=

Answer 1

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

Answer 2

g( x ) = ( X+3) / ( X^2 - 4) 

 

        Domain :

                        xε ( - ∞, -2) u ( -2 , +2) u ( +2 , + ∞)

 

  The X values of 

 

   X = -2 , and X = 2 is not in the domain of g, which is indicated in the Domain by proper sign which are

 Underlined.