If the range of g(x) is ( neg. infinity,4] and the domain of g(x) is ( neg. infinity, infinity), how do I find the domain of 1/g(x) - 5?

I came up with ( neg. infinity, -1) and ( 1, infinity). Is this correct? Thank you, Barbara

I am a student

I am reading 1/g(x) - 5 as ( ¹/_g(x)) - 5.

The only problem that can arise with your new function is if you have g(x) = 0, and hence ( ¹/_g(x)) - 5 is undefined since you can't divide by zero. Since the range of g(x) contains zero there might be an x so that g(x) = 0. Thus the domain of ( ¹/_g(x)) - 5 is all x in (minus infinity, infinity) except any x for which g(x) = 0.