PROBLEMS ON COMPOSITION OF FUNCTIONS FROM A GRAPH

Answer the following, using the graph below.

Problem 1 :

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

Solution:

(a) g(2) :

The value of g(2) from the graph of g(x) is 5.

So, g(2) = 5.

(b) f(g(2)) :

The value of g(2) from the graph of g(x) is 5.

So, f (g(2)) = f(5)

Value of f(5) from the graph f(x) is 0.

Then, the value of f (g(2)) is 0.

(c) f(2) :

The value of f(2) from the graph of f(x) is 0.

So, f(2) = 0.

(d) g(f(2)) :

The value of f(2) from the graph of f(x) is 0.

So, g (f(2)) = g(0)

Value of g(0) from the graph g(x) is 3.

Then, the value of g (f(2)) is 3.

Problem 2 :

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

Solution:

(a) g(0) :

The value of g(0) from the graph of g(x) is 3.

So, g(0)) = 3

(b) f(g(0)) :

The value of g(0) from the graph of g(x) is 3.

So, f (g(0)) = f(3)

Value of f(3) from the graph f(x) is -1.

Then, the value of f (g(0)) is -1.

(c) f(0) :

The value of f(0) from the graph of f(x) is 2.

So, f(0)) = 2

(d) g(f(0)) :

The value of f(0) from the graph of f(x) is 2.

So, g (f(0)) = g(2)

Value of g(2) from the graph g(x) is 5.

Then, the value of g (f(0)) is 5.

Problem 3 :

(a) (f ∘ g)(-3)      (b) (g ∘ f)(-3)

Solution:

(a) (f ∘ g)(-3) :

(f ∘ g)(-3) = f[g(-3)]

The value of g(-3) is 0.

f[g(-3)] = f(0)

The value of f(0) is 2.

(f ∘ g)(-3) = 2

(b) (g ∘ f)(-3) :

(g ∘ f)(-3) = g[f(-3)]

The value of f(-3) is 4.

g[f(-3)] = g(4)

The value of g(4) is 6.

(g ∘ f)(-3) = 6

Problem 4 :

(a) (f ∘ g)(-1)      (b) (g ∘ f)(-1)

Solution:

(a) (f ∘ g)(-1) :

(f ∘ g)(-1) = f[g(-1)]

The value of g(-1) is 2.

f[g(-1)] = f(2)

The value of f(2) is 5.

(f ∘ g)(-1) = 5

(b) (g ∘ f)(-1) :

(g ∘ f)(-1) = g[f(-1)]

The value of f(-1) is 2.

g[f(-1)] = g(2)

The value of g(2) is 5.

(g ∘ f)(-1) = 5

Problem 5 :

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

Solution:

(a) (f ∘ f)(3) :

(f ∘ f)(3) = f[f(3)]

The value of f(3) is -1.

f[f(3)] = f(-1)

The value of f(-1) is 3.

(f ∘ f)(3) = 3

(b) (g ∘ g)(-2) :

(g ∘ g)(-2) = g[g(-2)]

The value of g(-2) is 1.

g[g(-2)] = g(1)

The value of g(1) is 4.

(g ∘ g)(-2) = 4