Question

Which description best explains the domain of (g(f(x))?

the elements in the domain of f(x) for which g(f(x)) is defined
the elements in the domain of f(x) for which g(f(x)) is not zero
the elements in the domain of g(x) for which g(f(x)) is defined
the elements in the domain of g(x) for which g(f(x)) is not zero

Answer 1

Option: 1 is the correct answer.

• The elements in the domain of f(x) for which g(f(x)) is defined.

Explanation:

We are given two function f(x) and g(x) in terms of a single variable x.

The composition of the function is here given by:

(g(f(x))

We are asked to find the domain of this composition function.

We know that the domain of any function is the set of possible x-values where the function is well defined.

So, the domain of the function is the set of those x-values for which f(x) is defined and thus at that point the function g(f(x)) is also defined.

So, the correct answer is:

The elements in the domain of f(x) for which g(f(x)) is defined.

Answer 2

We will solve this question by taking two functions :

f(x) = x² and g(x) =
`(x^2)/(x -2)`

As , domain of f(x) is set of all real numbers,

And domain of g(x) is all real numbers except 2.

Now g[f(x)]= g(x²)=
`(x^2)/(x^2-2)`

Domain of g[f(x)] is all real numbers except √2 and -√2.

The Description which best describes about the domain of g[f(x)] is :

the elements in the domain of f(x) for which g(f(x)) is defined which is option 1.