EVALUATE THE INDICATED VALUE OF COMPOSITION FUNCTION FROM THE TABLE

Problem 1 :

Evaluate the indicated expression assuming that f, g, and h are the functions completely defined by the tables below :

(i)  (f o g) (1) 

(ii)  (f o g) (3)

(iii)  (g o f) (1)

(iv)  (g o f) (3) 

(v)  (f o f) (2)  

(vi) (f o g o h) (2)  

(vii)  (h o g o f) (2)

Solution :

(i)  (f o g) (1)

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

= f(2)

= 1

(ii)  (f o g) (3)

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

= f(1)

= 4

(iii)  (g o f) (1) 

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

= g(4)

= 3

(iv)  (g o f) (3)

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

= g(2)

= 1

(v)  (f o f) (2)

(f o f) (2) = f[f(2)]

=  f(1)

= 4

(vi) (f o g o h) (2)

(f o g o h) (2) = (f o g)[h(2)]

= (f o g) (3)

= f[g(3)]

= f(1)

= 4

(vii)  (h o g o f) (2)

(h o g o f) (2) = (h o g)[f(2)]

= (h o g) (1)

= h[g(1)]

= h(2)

= 3

Problem 2 :

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

a)   (f o g) (1)

b)   (f o g) (2)

c)   (g o f) (2)

d)   (g o f) (3)

e)  (g o g) (1)

f)  (f o f) (3)

Solution :

a) (f o g) (1) = f[g(1)]

From the table, the value of g(1) is 0.

= f(0)

The value of f(0) is 5

= 5

So, the value of (f o g) (1) is 5.

b)   (f o g) (2) = f[g(2)]

The value of g(2) is -3. Applying that

= f(-3)

The value of f(-3) is 11

= 11

So, the value of  (f o g) (2) is 11.

c)   (g o f) (2) = g[f(2)]

The value of f(2) is 1. Applying that,

= g(1)

The value of g(1) is 0

So, the value of (g o f) (2) is 0.

d)   (g o f) (3) = g[f(3)]

The value of f(3) is -1. applying that

= g(-1)

The value of g(-1) is 0.

So, the value of (g o f) (3) is 0.

e)  (g o g) (1) = g[g(1)]

The value of g(1) is 0. applying that

= g(0)

The value of g(0) is 1.

So, the value of (g o g) (1) is 1.

f)  (f o f) (3) = f[f(3)]

The value of f(3) is -1.

= f[-1]

The value of f(-1) is 7.

So, the value (f o f) is 7.

The accompanying tables define functions f and g.

Problem 3 :

What is (g o f)(3) ?

a) 6     b) 2      c) 8      d) 4

Solution :

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

From the table, the value of f(3) is 5.

= g(5)

The value of g(5) is 8.

So, the value of (g o f)(3) is 8. So, option c is correct.

Problem 4 :

Use the table of values to evaluate each expression 

Solution :

a) f(g(8))

The value of g(8) from the table, we get g(8) = 4

= f(4)

The value of f(4) is 4.

So, the value of f(g(8)) is 4.

b)  f(g(5))

From the table, the value of g(5) is 8.

= f(8)

The value of f(8) is 9.

So, the value of f(g(5)) is 9.

c)  g(f(5))

From the table, the value of f(5) is 0.

= g(0)

The value of g(0) is 9.

So, the value of g(f(5)) is 9.

d)  g(f(3))

From the table, the value of f(3) is 8.

= g (8)

The value of g(8) is 4.

So, the value of g(f(3)) is 4.

e)  f(f(4))

The value of f(4) is 4

= f(4)

The value f(4) is 4.

So, the value of f(f(4)) is 4.

f)  f(f(1))

The value of f(1) is 6.

= f(6)

The value of f(6) is 2.

So, the value of f(f(1)) is 2.

g)  g(g(2))

The value of g(2) is 6.

= g(6)

The value of g(6) is 7.

So, the value of g(g(2)) is 7.

h)  g(g(6))

The value of g(6) is 7.

= g(7)

The value of g(7) is 3.

So the value of g(g(6)) is 3.

Problem 5 :

Functions f and g consist only of the ordered pairs shown. Find the ordered pairs for y = f(g(x)).

f: (−12, 11), (−4, 9), (1, 3), (2, −4), (6, −5)

g: (−10, 6), (−3, 1), (0, −4), (5, 2), (8, −12)

Solution :

y = f(g(x))

Inputs are from the function g.

When x = 8

y = f(g(8))

y = f(-12)

y = 11

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.