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Determine the domain of each of the following functions.
f( x ) = x - 4 / x2 - 2 x -15
Solution
With this problem we have to avoid division by zero and thus we have to determine where the denominator is zero that means solving,
x2 - 2 x -15 = ( x - 5) ( x + 3) =0
⇒ x = -3, x = 5
Thus, these are the only values of x that we have to avoid and therefore the domain is,
Domain: All real numbers except x = -3 & x = 5
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