Question

The domain of f(x) is the set of all real values except 7, and the domain of g(x) is the set of all real values except -3. Which of the

following describes the domain of (gof)(x)?
all real values except X -3 and the x for which fex) 7
all real values except X -3 and the x for which f(x) -3
all real values except x 7 and the x for which f(x) 7
all real values except x * 7 and the x for which f(x) -3

Answer 1

Third choice

Explanation:

The domain of f(x) is the set of all real values except 7, i.e
`x\\e7`

and the domain of g(x) is the set of all real values except -3, i.e
`x\\e -3`

The domain of
`g\circ f` is the set of all real numbers x in the domain of
`f` such that
`f(x)` is in the domain of
`g(x)`.

However any numbers that are excluded from the domain of f must also be excluded from the domain of
`g\circ f`.

Therefore the correct choice is all real values except x=7 and the x for which f(x) =7