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 (g.f)(x)

Answer 1

The set of all real values except 7

Explanation:

We are given that,

Domain of the function f(x) is 'the set of all real values except 7'.

Domain of the function g(x) is 'the set of all real values except -3'.

It is required to find the domain of
`(g\circ f)(x)`.

Now, we know that,

The composition
`(g\circ f)(x)` of functions
`f(x)` and
`g(x)` will be defined where the function
`f(x)` is defined.

Since, the domain of f(x) is 'the set of all real values except 7'.

Thus, the domain of
`(g\circ f)(x)` is also 'the set of all real values except 7'.