# 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) = 15x^{2} + 6x – 5x – 2

(f•g)(x) = 15x^{2} + x – 2

**Example:**

f(x) = | 9x + 6 | |

2 |

g(x) = | 4 | |

6x + 4 |

Find function (f•g)(x)

(f.g)(x) = | 9x + 6 |
| ||||

2 |

(f.g)(x) = | 3(3x + 2) |
| ||||

2 |

= | 3 |
| ||||

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)

= 7x^{2} – x + 35x – 5

(f•g)(x) = 7x^{2} + 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) = 9x^{2} + 21x

g(x) = 3x + 7

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

**Solution:**

(f/g)(x) = | 9x^{2} + 21x | |

3x + 7 |

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

3x + 7 |

(f/g)(x) = 3x

(f/g)(15) = 3•15

= 45

RISE KNOWLEDGE

31/08/2018

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