Function Operations

Mathematics lesson, functions subject. Operations on functions. Addition, subtraction, multiplication and division operations with functions. Subject expression and solved questions.


Addition Of Functions 

A and B are two set that are not empty and have at least one common element.


f:A → R, 

g: B → R 

(f +g ): A∩B → R

 (f + g)(x) = f(x) + g(x) tir.

Sum of the functions f and g is a function that defined to the real numbers set from intersection set of these two set.

To add the functions given in polynomial form, each term of given functions is added.


Example:

f(x) = 12x – 6 

g(x) = 8x + 5

What is sum of the functins f(x) and g(x)?


Solution: 

(f + g)(x) = f(x) + g(x)

(f + g)(x) = 12x – 6 + 8x + 5

(f + g)(x) = 20x – 1 


Example:

f(x) = 7x + 3

g(x) = 5x – 2 

What is the result of the (f – g)(5)?


Solution:

Firstly, Let we do (f – g)(x) operation.

(f – g)(x) = f(x) – g(x)

(f – g)(x) = 7x + 3 – (5x – 2)

(f – g)(x) = 2x + 5

For x = 5,

(f – g)(5) = 2•5 + 5 

= 15


Example:

A = {2, 5, 9, 13, 15, 20}

B = {3, 5, 11, 15, 18, 22}

f(x) = 2x + 1

g(x) = x – 2 


Find the set of the sum of the functions f + g.


Solution:

Intersection set of the sets A and B.

C = {5, 15}

The numbers 5 and 15 are common elements in set A and B.

f(x) + g(x) = 2x + 1 + x – 2 

f(x) + g(x) = 3x – 1 

Suppose, the sum set of the f + g functions is D.

d1 = 3•5 – 1

d1 = 14

d2 = 3•15 – 1

d2 = 44

D = {14, 44}


Multiplication of Functions

A and B are two set that are not empty and have at least one common element.

f: A → R, 

g: B → R 

 A∩B ≠ Ø 

(f•g): A∩B → R

(f • g)(x) = f(x)•g(x) tir.

Multiplication of the functions f and g is a function that defined to the real numbers set from intersection set of the A and B set.

To multiply the functions given in polynomial form, each term of the functions is multiplied by each other.


Example:

f(x) = 3x – 1 

g(x) = 5x + 2


Find the (f•g)(x) function.


Solution:

(f•g)(x) = f(x) • g(x)

(f•g)(x) = (3x – 1 )(5x + 2)

(f•g)(x) = 15x2 + 6x – 5x – 2

(f•g)(x) = 15x2 + x – 2 


Example:

f(x) = 9x + 6
2




g(x) = 4
6x + 4




Find function (f•g)(x)


(f.g)(x) = 9x + 6 
4
6x + 4
2




(f.g)(x) = 3(3x + 2) 
4
2(3x + 2)
2





=3 
4
2
2




= 3


Example:

f(x) = x + 5

g(x) = 7x – 1


What is result of the (f•g)(2)?


Solution:

(f•g)(x) = (x + 5)(7x – 1)

= 7x2 – x + 35x – 5

(f•g)(x) = 7x2 + 34x – 5

(f.g)(2) = 7•4 + 34•2 – 5

= 91


Division Of Functions

A and B are two set that are not empty and have at least one common element.


f: A → R,

 g: A → R 

 A∩B ≠ Ø 

(f/g) : A∩B → R

(f/g)(x) = f(x)/ g(x) tir. (g(x) ≠ 0)


Division of the functions f and g is a function that defined to the real numbers set from intersection set of the A and B set.

Example:

f(x) = 12x + 8

g(x) = 4x + 12


Find the value of the (f:g)(6)


Solution:

(f:g)(x) = f(x) /g(x)

(f:g)(x) = 12x + 8
4x + 12




(f:g)(x) = 4(3x + 2)
4(x + 3)




(f:g)(x) = 3x + 2
x + 3




(f:g)(6) = 3•6 + 2
6 + 3




(f:g)(6) = 20
9




Example:

f(x) = 9x2 + 21x

g(x) = 3x + 7 

Find value of the (f/g)(15)


Solution:

(f/g)(x) = 9x2 + 21x
3x + 7




(f/g)(x) = 3x(3x + 7)
3x + 7





(f/g)(x) = 3x

(f/g)(15) = 3•15

= 45


Compound Functions



RISE KNOWLEDGE

31/08/2018

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