Question

Helppppppppppppppppppppp

Answer 1

The domain of a composite function
`f(g(x))` is, technically speaking, the set of those inputs
`x` in the domain of
`g` for which
`g(x)` is in the domain of
`f`. What this is really saying, though, is that the domain is for those
`x` that overlap in both functions, or that are defined for both
`f(x)` and
`g(x)`. You can write {
`x \ | \ D_f` ∩
`D_g`}.

For this specific example, the domain of
`f(x)` is {all real numbers
`x`}. The domain of
`g(x)` is {
`x \ | \ x \\eq 13`}. These overlap for all
`x` such that
`x \\eq 13`, so the domain of
`f(g(x))` is {
`x \ | \ x \\eq 13`}.

Answer 2

The first thing you should do in this case is to compose both functions:
f (x) = x + 7
g (x) = 1 / (x-13)
Making the composition
f (g (x)) = (1 / (x-13)) + 7
f (g (x)) = (7 (x-13) +1) / (x-13)
Answer:
The domain of the function is:
x other than 13
(option 4)