Question

Find the domain of the rational expression. f(x) = (x + 7)(x-4)

Answer 1

If you wrote the expression correctly, then

$f(x)=(x+7)(x-4)=x^2+3x-28$

Is a polynomial, and thus defined everywhere: its domain is the set of all real numbers.

If, by chance, you meant

$f(x)=\dfrac{x+7}{x-4}$

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.