The domain of the function fx lnx 5x 7 is 5 infinity 5 7

The domain of the function f(x) = ln(x - 5)/x - 7 is (5, infinity) (5, 7) union (7, infinity) (7, infinity) (-infinity, 5) union (7, infinity) (-infinity, 7) union (7, infinity)

Solution

f(x)=ln(x-5)/(x-7)

ln can take only positive values

therefore x-5>0

x>5

(5,infinity)

And in a rational function,the bottom cant be zero

And at x=7 the bottom is zero

Therefore domain is

(5,7)U(7,inf)

Correct answer is b.