Answer:
Two functions f(x) and g(x) are inverses if and only if:
f( g(x) ) = x
and
g( f(x) ) = x
In this case, we have:
f(x) = 1*x - 6
g(x) = 6*x + 1
Let's check if the functions are inverses.
f( g(x) ) = 1*g(x) - 6 = 1*(6x + 1) - 6 = 6x + 1 - 6 = 6x - 5
and
g( f(x) ) = 6*f(x) + 1 = 6*(1x - 6) + 1 = 6x - 36 + 1 = 6x - 35
So we can see that:
f( g(x) ) ≠ x
g( f(x) ) ≠ x
Thus, f(x) and g(x) are not inverses.
Particularly, the two compositions are:
f( g(x) ) = 6x - 5
g( f(x) ) = 6x - 35
Both of these are linear functions, thus the domain in both cases is the set of all real numbers, that can be written as:
domain = (-∞, ∞)
