SOLUTION: Determine the value(s) of the variable that must be excluded from the domain. f(x) = {{{x^2

SOLUTION: Determine the value(s) of the variable that must be excluded from the domain. f(x) = {{{x^2 - 16)/(-9x^2 + 27x + 36)}}}

Question 656250: Determine the value(s) of the variable that must be excluded from the domain.
f(x) =

Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!

f(x) = 

The denominator must not be 0

-9x� + 27x + 36 ≠ 0

-9(x� - 3x - 4) ≠ 0

   -9(x-4)(x+1) ≠ 0

   x - 4 ≠ 0;  x + 1 ≠ 0
       x ≠ 4;      x ≠ -1

 The graph looks like this:



There is no point where x=-1 because there is a vertical 
asymptote there, and there is a hole in the curve, and
therefore no point at (4,-), where the little circle is.
So -1 and 4 are excluded from the domain.

The domain is

(-,-1) U (-1,4) U (4,)

Edwin

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