Math Domain question

g(x)=√2/(x-3)

G(x)= ln(x-2)

Find the domain of g(x) and G(x)
Can you please do step by step thank you..

Since x-3 is in the denominator, the only restricion on it is that it can't be zero. So x can't be 3. The domain is R - {3}. This is also written as R\{3}.

ln is only defined for positive numbers. So we need x - 2 > 0. So the domain is (2, inf).