FROM THE TABLE OF VALUES FOR FUNCTIONS EVALUATE THE COMPOSITE FUNCTION

To find composition of functions from the table of values given, let us look at the example.

(f ∘ g)(x) = f [g(x)]

• x is the input. From the table, find the output for the function g.
• Let g(x) = a
• Now the original function will become f [a].
• Now a is the input. From the table, find the output for the function f.

(f ∘ g)(-1) = f [g(-1)]

When -1 is the input, calculating the value of the function g, we get

(f ∘ g)(-1) = f [-2]

When the input is -2, the value of the function f, we get

(f ∘ g)(-1) = 2

Using a table to find the value of a composite function.

Problem 1 :

Use the table to find the indicated function values.

Solution:

1.

f(g(3))

When 3 is the input, calculating the value of the function g, we get

f(g(3)) = f [0]

When the input is 0, the value of the function f, we get

f(g(3)) = 3

2.

f(g(1))

When 1 is the input, calculating the value of the function g, we get

f(g(1)) = f [-1]

When the input is -1, the value of the function f, we get

f(g(1)) = 1

3.

g(f(-2))

When -2 is the input, calculating the value of the function f, we get

g(f(-2)) = g[2]

When the input is 2, the value of the function g, we get

g(f(-2)) = -8

4.

g(f(-1)) 

When -1 is the input, calculating the value of the function f, we get

g(f(-1)) = g[1]

When the input is 1, the value of the function g, we get

= -1

5.

g(f(0)) 

When 0 is the input, calculating the value of the function f, we get

g(f(0)) = g[3]

When the input is 3, the value of the function g, we get

g(f(0)) = 0

6.

g(g(-2))

When -2 is the input, calculating the value of the function g, we get

g(g(-2)) = g[3]

When the input is 3, the value of the function g, we get

= 0

7.

f(f(0)) 

When 0 is the input, calculating the value of the function f, we get

f(f(0)) = f[3]

When the input is 3, the value of the function f, we get

= 19

8.

g(f(1)) 

When 1 is the input, calculating the value of the function f, we get

g(f(1)) = g[-1]

When the input is -1, the value of the function g, we get

= -2

Problem 2 :

The functions f(x) and g(x) are defined by the tables below.

1.f(g(5)) =

2. f(g(1)) = 

3. g(f(4)) =

4. f(f(1)) = 

Solution:

1.

f(g(5)) 

When 5 is the input, calculating the value of the function g, we get

f(g(5)) = f[2]

When the input is 2, the value of the function f, we get

= 11

2. 

f(g(1)) 

When 1 is the input, calculating the value of the function g, we get

f(g(1)) = f[3]

When the input is 3, the value of the function f, we get

= 10

3.

g(f(4)) 

When 4 is the input, calculating the value of the function f, we get

g(f(4)) = g[8]

When the input is 8, the value of the function g, we get

= 0

4.

f(f(1)) 

When 1 is the input, calculating the value of the function f, we get

f(f(1)) = f[4]

When the input is 4, the value of the function f, we get

= 8

Problem 3 :

Use the tables of the functions f and g.

1. (f ∘ g)(-7)

2. f(g(0))

3. (f ∘ g)(4)

Solution:

1. 

(f ∘ g)(-7) = f(g(-7))

When -7 is the input, calculating the value of the function g, we get

f(g(-7)) = f[4]

When the input is 4, the value of the function f, we get

(f ∘ g)(-7) = 3

2.

f(g(0)) 

When 0 is the input, calculating the value of the function g, we get

f(g(0)) = f[-2]

When the input is -2, the value of the function f, we get

= 9

3.

(f ∘ g)(4) = f(g(4))

When 4 is the input, calculating the value of the function g, we get

f(g(4)) = f[6]

When the input is 6, the value of the function f, we get

(f ∘ g)(4) = -10

Problem 4 :

The functions A(x) and B(x) are defined by the tables below.

a) A(B(4)) = ___

b) B(A(1)) = ___

c) B(A(7)) = ___

d) A(B(1)) = ___

Solution:

a)

A(B(4)) 

When 4 is the input, calculating the value of the function B, we get

A(B(4)) = A[6]

When the input is 6, the value of the function A, we get

= 11

b)

B(A(1)) 

When 1 is the input, calculating the value of the function A, we get

B(A(1)) = B[7]

When the input is 7, the value of the function B, we get

= 15

c)

B(A(7)) 

When 7 is the input, calculating the value of the function A, we get

B(A(7)) = B[3]

When the input is 3, the value of the function B, we get

= 2

d)

A(B(1)) 

When 1 is the input, calculating the value of the function B, we get

A(B(1)) = A[0]

When the input is 0, the value of the function A, we get

= 5