Showing posts with label real numbers. Show all posts
Showing posts with label real numbers. Show all posts

Friday, May 3, 2013

Functions for Math

Introduction to functions for math
The mathematical concept of a function expresses the intuitive idea that one quantity completely determines another quantity (the value, or the output). A function assigns a unique value to each input of a specified type. The argument and the value may be real numbers, but they can also be elements from any given sets: the domain and the codomain of the function (Source: Wikipedia)

I like to share this prime numbers from 1 to 100 with you all through my article.

Functions for math


An illustration of a function through the real numbers since equally its domain also the codomain is the function f(x) = 4x.

This gives to all real number the real number that is to say twice as big.

In this example, we be able to inscribe f(6) = 24.

The domain of the function is the set of every acceptable input to a specified function.

The image or else range of the function is the set of every resultant outputs.

The representation is frequently a subset of various larger set, called the codomain of a function. consequently such as, the function f(x) = x2 might obtain since its domain the set of every real numbers as its representation the set of every non-negative real numbers, as well as its codomain the set of every real numbers.

Understanding Regression Analysis Example is always challenging for me but thanks to all math help websites to help me out.

Examples for functions math


Example 1

If f (2, 7) = 57 and f(1, 6) = 37, what is the value of (4, 10)?

Solution

The function f (a, b) = a^3 + b^2

f (2, 7) t is = 2^3 + 7^2 = 8 + 49 = 57
f (1, 6) = 1^3 + 6^2 = 1 + 36 = 37.

Therefore, f (4, 10) = 4^3 + 10^2 = 64 + 100 = 164.

The value of (4, 10) = 164

Example 2

Suppose the given function f(x) is 6x+7. Finding the value of f (3) and f(7)?

Solution

Given function f(x) = 6x+7

Find the value of f (3)

Substitute the value x for 3, then

f (3) = 6x3+7

=18+7

f (3) = 25

Find the value of f (7)

Substitute the value x for 7, then

f (7) = 6x7+7

=42+7

f (7) = 49

Monday, February 4, 2013

Sum of Reciprocals

Introduction:-

The  reciprocal for a number x, denoted by  `1/x`  or x ^−1, is a number which when multiplied by x yields the multiplicative identity 1. The reciprocal of a fraction `a/b` is `b/a` . For the reciprocal of a real number, divide 1 by the number. For example, the reciprocal of 8 is  one fifth (`1/8` or 0.2), and the reciprocal of 0.25 is (`"1/0.25` or 4).                                                                      Source: - Wikipedia

Sum of Reciprocals

The following are the steps used to find sum of reciprocals:-

Step 1 The first step in finding the sum of reciprocal of a two numbers is to find the reciprocal of the given numbers.

Step 2 Then we need to add the reciprocal of these two numbers.

Find the Sum of reciprocal of real numbers a and b.

As per step 1we need to find the reciprocal of a and b.

The reciprocal of a is `1/ a.`

The reciprocal of b is `1/ b.`

Now according to step 2 we add two reciprocals 1/ a and 1/ b.

Sum of reciprocals of a and b is `1/ a + 1/ b` .

Find the Sum of reciprocal of fractions` a/ b` and `c/ d.`

As per step 1we need to find the reciprocal of `a/b` and `c/ d.`

The reciprocal of `a/b` is `b/ a.`

The reciprocal of `c/d` is `d/ c` .

Now according to step 2 we add two reciprocals `b/ a` and `d/ c.`

Sum of reciprocals of `a/b` and `c/ d` is `b/ a + d/ c.`

Please express your views of this topic Continuous Probability Distribution Example by commenting on blog.

Solved Problems:-

Problem 1:-

Find the sum of reciprocal of 2 and 3.

Solution:-

The given two numbers are 2 and 3.

We need to find the sum of their reciprocals.

To find the sum of reciprocals we first need find the reciprocal of given two numbers.

The reciprocal of 2 is `1/2.`

The reciprocal of 3 is `1/ 3.`

Now we can we need to add these two reciprocal values

`= ` `1/ 2+ 1/ 3.`

By taking LCM of 2 and 3 we get 6

`= (3 + 2 )/6`

`= 5/ 6.`

The sum of reciprocal of 2 and 3 is `5/ 6`

Problem 2:-

Find the sum of reciprocal of two fractions  `1/ 3 ` and `3/ 4.`

Solution:-

The given two numbers are `1/ 3` and `3/ 4.`

We need to find the sum of their reciprocals.

To find the sum of reciprocals we first need find the reciprocal of given two numbers.

The reciprocal of `1/ 3` is `3/ 1.`

The reciprocal of `3/ 4` is ` 4 / 3.`

Now we can we need to add these two reciprocal fraction values

= `3/ 1+ 4/ 3.`

By taking LCM of 1 and 3 we get 3.

`= (9 + 4 )/3`

`= 13/ 3.`

The sum of reciprocal of `1/ 3` and `3/ 4.` is `13 / 3`