What is the domain of f(x) = √(x-4)x-7?

Two separate restrictions apply. The square root needs $x-4\ge0$, so $x\ge4$. The denominator cannot be zero, so $x\ne7$. Both must hold, so the domain is $x\ge4$ with $x\ne7$, choice J. Choice F keeps only the square-root condition and allows $x=7$, where the fraction is undefined. Choice G keeps only the denominator condition and allows values like $x=0$, where the square root is not real. Choice H uses $x>4$, which wrongly excludes $x=4$; at $x=4$ the numerator is $\sqrt0=0$ and the denominator is $-3$, so $f(4)=0$ is defined.