The application of one function followed by the application of a second function to the result of the first as in F^-1(f(x)) is called composition of functions. The two functions need not be inverse of each other. In a diagram, the output of one function is f(x) is used as the input for a second function g(x). In this case, the composite is denoted g(f(x)) which is read "g composed with f of x" or "g of f of x."
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Suppose f and g are functions defined by the following table:
x) -3 -2 -1 0 1 2 3
f(x) 10 8 7 3 -4 -7 -8
g(x) 3 1 0 2 -3 -1 -2
i. Make a table of values for f(g(x)) with x= -3,-2,-1,0,1,2,3 Remember to always start with the innermost set of parentheses
ii. Make a table of values for g(g(x)) with x= -3,-2,-1,0,1,2,3.
iii. Explain why you cannot find the composite function g(f(x)).
a)Consider the two functions f(x)=-x^2+ 7 and g(x)=3x+4. Using input values of -1,2,0.5,and 8 for x:
1. Calculate f(g(x)) for each input value
2. Calculate g(f(x)) for each input value.
B) if f and g are two functions, what must be true about the domains and ranges of f and g in order for f(g(x)) to make sense? What must be true for g(f(x))to make sense?
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