Composition of function :
If f and g are functions, then the composite function of f and g is defined by
(f ∘ g)(x) = f( g(x) )
The domain of (f ∘ g) is the set of all real numbers x in the domain of g such that ݃g(x) is in the domain of f.
Functions f and g are defined as shown in the table below.
Use the information above to complete the following tables. (Some answers may be undefined.)
Problem 1 :
Solution:
When x = 0,
f(g(x)) = f(g(0))
= f(4)
= 7
When x = 1,
f(g(x)) = f(g(1))
= f(5)
= undefined
When x = 2,
f(g(x)) = f(g(2))
= f(0)
= 2
When x = 4,
f(g(x)) = f(g(4))
= f(1)
= 4
Problem 2 :
Solution:
When x = 0,
g(f(x)) = g(f(0))
= g(2)
= 0
When x = 1,
g(f(x)) = g(f(1))
= g(4)
= 1
When x = 2,
g(f(x)) = g(f(2))
= g(4)
= 1
When x = 4,
g(f(x)) = g(f(4))
= g(7)
= undefined
Problem 3 :
Solution:
When x = 0,
f(f(x)) = f(f(0))
= f(2)
= 4
When x = 1,
f(f(x)) = f(f(1))
= f(4)
= 7
When x = 2,
f(f(x)) = f(f(2))
= f(4)
= 7
When x = 4,
f(f(x)) = f(f(4))
= f(7)
= undefined
Problem 4 :
Solution:
When x = 0,
g(g(x)) = g(g(0))
= g(4)
= 1
When x = 1,
g(g(x)) = g(g(1))
= g(5)
= undefined
When x = 2,
g(g(x)) = g(g(2))
= g(0)
= 4
When x = 4,
g(g(x)) = g(g(4))
= g(1)
= 5
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