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)?
1)) all real values except X-3 and the x for which f(x)7
2)) all real values except X-3 and the x for which f(x)=-3
3)) all real values except x 7 and the x for which f(x) 7
4)) all real values except x 7 and the x for which f(x) -3

Answer 1

Answer:

The option is: all real values except x = 7 and the x for which f(x) = -3

Step-by-step explanation:

As the domain of f(x) is the set of all real values except 7. So it can be written as follows:

              Domain of f(x) = { x ∈ R | x ≠ 7}

As the domain of g(x) is the set of all real values except -3. So it can be written as follows:

              Domain of g(x) = { x ∈ R | x ≠ -3}

It is a common rule that the domain of a composite function (gºf)(x) will be the set of those input x in the domain of f for which f(x) is in the domain of g.

So, the option is: all real values except x = 7 and the x for which f(x) = -3

Keywords:  domain, composite function

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