what is the domain of f[g(x)]?
A.all the elements x in the domain of g for which g(x) is in the domain of f
B.the range of x
To determine the domain of the composite function f[g(x)], we need to consider the composition of two functions, f and g.
The composite function f[g(x)] is formed by substituting the value of g(x) into the function f.
For the composite function to be defined, two conditions must be met:
1. g(x) must be within the domain of the function f.
2. x must be within the domain of the function g.
Therefore, the correct answer is A: all the elements x in the domain of g for which g(x) is in the domain of f.
In other words, the domain of f[g(x)] consists of all the values of x for which both x is in the domain of g and g(x) is in the domain of f.