What is the domain of the function #f(x)=(3x^2)/(x^2-49)#?
The domain of a function is the set of the values in which you can calculate the function itself.
The problem of finding the domain of a functions is due to the fact that not every function "accepts" every real number as an input.
If you have a rational function, you must exclude from the domain the values for which the denominator is zero, since you cannot divide by zero. So, for example, if you consider the function
In your case, the denominator is the function
These are the only two values you have to consider, since for any other
With a proper notation, your domain is the set