Question 564954: The functions f and g are defined by these sets of input and
output values.
g = {(1, 2), (– 2, 4), (5, 5), (6, – 2)}
f = {(2, 1), (4, – 2), (5, 5), (– 2, 6)}
a. Find g( f (2)).
b. Find f (g(6)).
c. Select any number from the domain of either g or f, and find f (g(x)) or g( f (x)), respectively. Describe what is happening.
Answer by issacodegard(60)   (Show Source):
You can put this solution on YOUR website! The elements of the functions are of the form (input, output). So, find the ordered pair in f that has an input value of 2. It's (2,1). In other words, f(2)=1. So g(f(2))=g(1). Find the element of g that has an input value of 1. It's (1,2), so g(1)=2. Therefore, g(f(2))=2.
The domain of f is {2,4,5,-2} and the domain of g is {1,-2,5,6}, and the ranges of f and g are {2,4,5,-2} and {1,-2,5,6} respectively. All the parts are similar, and knowing the domains and ranges of the functions should help you with understanding the composite functions.
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