EVALUATING COMPOSITION OF FUNCTIONS FROM A GRAPH WORKSHEET

Answer the following, using the graph below.

composition-function-graph.png

Problem 1 :

(a) g(2)    (b) f(g(2))     (c) f(2)        (d) g(f(2))

Solution

Problem 2 :

(a) g(0)           (b) f(g(0))       (c) f(0)       (d) g(f(0))

Solution

Problem 3 :

(a) (f ∘ g)(-3)      (b) (g ∘ f)(-3)

Solution

Problem 4 :

(a) (f ∘ g)(-1)      (b) (g ∘ f)(-1)

Solution

Problem 5 :

(a) (f ∘ f)(3)         (b) (g ∘ g)(-2)

Solution

Answer Key

1)  a)  g(2) = 5    b)  f (g(2)) = f(5)    c)  f(2) = 0 

d)  g (f(2)) = 3.

2)  a)  g(0)) = 3   b)  f (g(0)) is -1    c)  f(0)) = 2

d)  g (f(0)) = 5

3)  a)  (f ∘ g)(-3) = 2       b)  (g ∘ f)(-3) = 6

4)  a)  (f ∘ g)(-1) = 5        b)  (g ∘ f)(-1) = 5

5)  a)  (f ∘ f)(3) = 3       b)  (g ∘ g)(-2) = 4

Problem 1 :

Refer to the graph to complete the statements below.

compositionfungraph

a) (f + g)(-3) = ______             Solution

b) (f · g)(2) = ______             Solution

c) (f/g)(-1) = ______          Solution

d) (f ∘ g)(3) = ______          Solution

e) g-1(-4) = ______           Solution

f) Evaluate (f ∘ f)(2) ______          Solution

g) Evaluate g(f(g(1))) ______        Solution

h) State the domain of f + g _____        Solution

i) State the domain of f/g. ______        Solution

j) Evaluate (f(3))3 - 4g(-2) ______       Solution

k) For what value(s) is f(x) = 3? _______     Solution

Answer Key

1)  a)  (f + g)(-3)  = -1

b)   (f · g)(2) = 0

c)  (f/g)(-1) = 2/(-3)

d)  (f ∘ g)(3) = 4

e)  g(x) = -4

f)  (f ∘ f)(2) = 2

g)  g(f(g(1))) = 0

h)  domain of f + g = [-3, 4]

i)  domain of f/g = [-3, 1] u (3, 4]

j)  (f(3))3 - 4g(-2) = 24

k)  For what value(s) is f(x) = 3?

-2, 0 and 2

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