EVALUATING COMPOSITION OF FUNCTIONS FROM TABLES

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. 

composition-function-q1

Use the information above to complete the following tables. (Some answers may be undefined.)

Problem 1 :

composition-function-q2.png

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 :

composition-function-q3.png

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 :

composition-function-q4.png

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 :

composition-function-q5.png

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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