If you wrote the expression correctly, then
[tex]f(x)=(x+7)(x-4)=x^2+3x-28[/tex]
Is a polynomial, and thus defined everywhere: its domain is the set of all real numbers.
If, by chance, you meant
[tex]f(x)=\dfrac{x+7}{x-4}[/tex]
Then we must exclude the point x=4 from the domain, since that value would cause the denominator to vanish. So, the domain would be the set of real numbers, minus the number 4.
