Question

given f(x)=x-3 and g(x)=1/x-4 find the domain and range of the following functions
f(x)

f(g(x))

f(f(x))

Answer 1

I will assume you meant g(x) = 1/(x-4)

for f(x) = x-3, the domain and range are both the set of R

f(g(x))
= 1/(x-4) - 3

domain: any R, x≠4
range : any R, y ≠ -3

f(f(x) = (x-3) - 3
= x -6

domain: any R
range : any R