EVALUATING COMPOSITION OF FUNCTIONS FROM TABLE WORKSHEET

Problem 1 :

Use the table of values to evaluate each expression

 1)  f ( g(8) )4)  g ( f (3) )7)  g ( g (2) ) 2)  f( g(5) )5)  f ( f (4) )8)  g ( g (6) ) 3)  g ( f (5) )6)  f ( f (1) )9)  g ( g (1) )

Solution

Problem 2 :

Evaluating Composite Functions :

The tables give some selected ordered pairs for functions f and g

 1) (f ∘ g)(2)2) (f ∘ g)(1)3) (f ∘ g)(9) 4) (f ∘ g)(5)5) (g ∘ f)(6)6) (f ∘ g)(7) 7) (g ∘ f)(12)8) (g ∘ f)(3)

Solution

Problem 3 :

Use the tables of ordered pairs to determine the value of each composite function

 1) (𝑓 ∘ 𝑔)(36) =2)  (𝑔 ∘ 𝑔)(16) = 3) (𝑔 ∘ 𝑓)(4) =4)  (𝑓 ∘ 𝑓)(4) =

Solution

Problem 4 :

The table below shows values of 𝑓(𝑥) at selected values of 𝑥. The function 𝑔(𝑥) is shown in the graph below.

Let h be the function defined by ℎ(𝑥) = 2|𝑥 − 4|.

Find:

 1. 𝑦 = ℎ(𝑓(2))2. 𝑦 = ℎ(𝑔(3))3. 𝑦 = 𝑔(𝑓(−2)) 4. 𝑦 = 𝑓(𝑔(−3))5. 𝑦 = 𝑔(𝑓(ℎ(3)))6. Find ℎ(𝑓(𝑔(0)))

Solution

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

Problem 5 :

 (i)  (f ∘ g) (1)(ii)  (g ∘ f) (2)(iii)  (g ∘ g) (1) (iv)  (f ∘ g) (2)(v)  (g ∘ f) (3)(vi)  (f ∘ f) (3)

Solution

Problem 6 :

(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

Problem 7 :

(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

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