Given : f (x) = 1/x+5 and g (x) = x-2 What are the restrictions of the domain of f (g (x)) ?

I don't know if it's (1/x) + 5 or 1 / (x+5) anyways

g (x) = x-2 so in f (g (x)) you replace every x with x-2

f (g (x)) = (1 / (x-2)) + 5 or 1 / (x-2-5) = 1 / (x-7)

if the function is like the first form so you avoid numbers which will make your denominator equals zero

x-2 = 0, x=2 or x-7 = 0, x=7

so if it's like first one answer is R - 2

if it's second answer is R - 7

The restrictions of the domain of f (g (x)) is x = - 3