Let = 3x – 6 and g(x) = x –2. Find and its domain. (1 point) Responses 3; all real numbers 3; all real numbers 3; all real numbers except x = 2 3; all real numbers except x = 2 1; all real numbers 1; all real numbers –3; all real numbers except x = 3
The composition of functions is obtained by substituting the expression for g(x) into the expression for f(x).
Let f(x) = 3x – 6 and g(x) = x – 2.
The composition f(g(x)) is found by substituting g(x) into f(x):
f(g(x)) = 3(g(x)) – 6
= 3(x – 2) – 6
= 3x – 6
Therefore, f(g(x)) = 3x – 6.
The domain of f(g(x)) is the same as the domain of g(x).
The domain of g(x) is all real numbers since there are no restrictions or undefined values.
So, the correct response is 3; all real numbers.