Find out the domain of each of the following functions.
g( x ) = x+3 /x^{2}+ 3x -10
Solution
The domain for this function is all of the values of x for which we don't have division by zero or the square root of a -ve number. If we remember these two ideas determining the domains will be pretty easy.
g( x ) = x+ 3 / x^{2}+ 3x -10
Thus, in this case there are no square roots therefore we don't have to worry about the square root of a -ve number. However, there is a possibility which we'll have a division by zero error. To find out if we will we'll have to set the denominator equal to zero and solve.
x^{2}+3x -10 = ( x + 5) ( x - 2) = 0 x= -5, x = 2
Thus, we will get division by zero if we plug in x = -5 or x= 2 . This means that we'll have to avoid those two numbers. Though, all the other values of x will work as they don't give division by zero. Then the domain is,
Domain: All real numbers except x = -5 & x = 2