find the domain of the following rational function
r(x)= 2(x2-6x-40)
3(x2-100)
Unless otherwise specified, we usually take the domain of a function to be all real numbers for which the function is defined.
So consider what values of would make undefined. Those are the values that are excluded from the domain. (Hint: look for values that would cause things like a division by zero or the taking of the square root/logarithm of a negative number).
Be careful. The domain is the values for which the function is defined. But when , the function is undefined (due to a division by zero). Thus your answer should be reversed: the domain is all real numbers not equal to . If you want to write this with set notation, there are several ways:
or
for example.