Answer:
We will solve this question by taking two functions :
f(x) = x² and g(x) = [tex]\frac{x^2}{x -2}[/tex]
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)= [tex]\frac{x^2}{x^2-2}[/tex]
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.
Answer:
Option: 1 is the correct answer.
Step-by-step 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.
