EVALUATING COMPOSITION OF FUNCTIONS FROM TABLE

Use the values in the table to evaluate the indicated composition of functions.

Example 1 :

Solution :

(i)  (f ∘ g) (1) = f [g(1)]

The value of g(1) from the table is 0. So replacing g(1) by 0.

 f [g(1)] = f(0)

The value of f(0) from the table is 5.

f(0) = 5

(ii)  (g ∘ f) (2) = g [f(2)]

The value of f(2) from the table is 1. So replacing f(2) by 1.

 g [f(2)] = g(1)

The value of g(1) from the table is 0.

g(1) = 0

(iii)  (g ∘ g) (1) = g [g(1)]

The value of g(1) from the table is 0. So replacing g(1) by 0.

 g [g(1)] = g(0)

The value of g(0) from the table is 1.

g(0) = 1

(iv)  (f ∘ g) (2) = f [g(2)]

The value of g(2) from the table is -3. So replacing g(2) by -3.

 f [g(2)] = f(-3)

The value of f(-3) from the table is 11.

f(-3) = 11

(v)  (g ∘ f) (3) = g [f(3)]

The value of f(3) from the table is -1. So replacing f(3) by -1.

 g [f(3)] = g(-1)

The value of g(-1) from the table is 0.

g(-1) = 0

(vi)  (f ∘ f) (3) = f [f(3)]

The value of f(3) from the table is -1. So replacing f(3) by -1.

 f [f(3)] = f(-1)

The value of f(-1) from the table is 7.

f(-1) = 7

Example 2 :

(i)  f(13)

(ii)  f(6)

(iii)  g(15)

(iv)  g(13)

(v)  For what value of x, f(x) = 35 ?

(vi)  For what value of x, g(x) = 5 ?

Solution :

(i)  f(13) = -19

(ii)  f(6) = 35

(iii)  g(15) = 23

(iv)  g(13) = 5

(v) f(x) = 35, when x = 6.

(vi) g(x) = 5, when x = 13.

Example 3 :

(i)  f(4) = 

(ii)  g(1) = 

(iii)  g(4) =

(iv)  g(-6) = 

(v) For what value of x, f(x) is -24 ?

(vi) For what value of x, f(x) is 4 ?

Solution :

(i)  f(4) = 16

(ii)  g(1) = -4

(iii)  g(4) = 10

(iv)  g(-6) = 14