#inverse of a function

[alwaysmathematics]

Sequences and functions

Generating sequences

A sequence is an ordered set of numbers/ terms arranged according to a specific rule. For example : 3, 7, 11, 15, 19. This sequence has 5 terms, in order according to a specific rule, added by 4.

There are two types of sequence:

Linear Sequence : each term will be increased or decreased by the same number. For example : 5.3, 4.5, 3.7

Non-Linear Sequence : each term will be increased or decreased by a different number. For example : 2, 4, 8, 16

Finding the nth term

You can find the value of a term based on its position. It is called as an nth term. The value of n is the position of the term. Here is the general way to construct the nth term of 3, 7, 11, 15, 19.

find the rule of the sequence

multiply it with the value of n

find the value of term before term position 1

place the result of step no 3 next to the result of step no 2

Now, we will execute them. (1) the rule of the sequence is "added by 4". (2) multiply it with the value of n, 4n. (3) find the value available before term position 1 is 3 - 4. The result is -1. (4) place the result of step no 3 next to the result of step no 2, 4n - 1. So the nth term of 3, 7, 11, 15, 19 is nth= 4n - 1

With this nth term, we can find the value of term in any position! For example, we want to know the value of term position 121 of the above sequence, 3, 7, 11, 15, 19. It means the value of n is 121. The nth term of this sequence is 4n - 1. Substitute the n with 121. It becomes nth term = (4 x 121) - 1. The result is 483. The value of term position 121 for this sequence is 483.

What will be nth term of 5.3, 4.5, 3.7? and find the value of term position 98. The answer of this question will given at the end of the post.

Finding the inverse of a function

Function can be in 3 different forms, an equation, a mapping and an function mapping. When you give an input to a function, you will get an output.

The example of function in the form of an equation is y = 3x - 2. From this equation, we can say " to get the value of y, we need to multiply the value of x by 3 and minus it by 2". The conclusion, x is the required input so that the function or the calculation can be executed in order to get the output, y.

The look of the mapping form for the same function is x → 3x - 2. The most left, x, is the input. The next one is the process should be done to the value of x (function) in order to get the output, y.

Above is the example of a function machine. X is the input to the function. The function will multiply the value of x by 3 and minus it by 2. The result of the function becomes the value of y. Y is the output.

The process or the function is read from left to right. When we read it in the opposite way, we can called it as inverse of the function. Here are the steps for inversing a function.

change the x to y and y to x

use the left arrow instead of right arrow

change the operation to the opposite one , minus to plus, plus to minus, multiply to divide, divide to multiply, square to square root, square root to square

Here is the result of inversing the function using a function machine.

The result of inverse the function :

in the form of equation is y = (x + 2)/3

in the form of mapping is x → (x + 2)/3

Work out the inverse function for y = (x + 1)/2. The answer of this question will given at the end of the post.

NOTE: When I want to find the inverse of the function, if it is possible, I will use a function machine. This question looks simple but if you don't understand well the function is and you don't know very well about the order of operations, you might make a mistake for this question.

The answer for:

What will be nth term of 5.3, 4.5, 3.7? nth = -0.8n + 6.1

find the value of term position 98. (-0.8 x 98) + 6.1 = -72.3

The inverse function for y = (x + 1)/2. y = 2x - 1

Thank you.

[vidyakul-blog]

Class 12 Maths Chapter 1 Relation and Function

[mathematicalanalysis-blog-blog]

inverse of a function

Inverse of a function is expressed as the reverse process of doing something that will take to the starting point from where we have started previously. It will be explained in simple words as undo process in which all the work done is going to its starting position. If we have some values that are given into the specific function and produce some output then inverse of function is define as a function in which we will enter the coming output and it gives the initial values.

We can express it in form of two expression as if there are two functions named as A and B that take an input c as A (c) then B (c) is inverse of function if A B (c) = c and B A (c) = x .

It is a process in which we find inverse value of the function and by putting one of value we get another value.

According to the definition of inverse of a function it is a set of ordered pairs and by interchanging the elements as (first element with second and vice versa) , get that set of ordered pair. If a function F (a) then its inverse function is expressed as F - 1 (a).

We can explain it as if a function F (a) = (a , b) , (c , d) , (e , f) then inverse of a function is denoted as F -1 (a) = (b , a) , (d , c) , (f , e).

How to Find Circumference of a Circle is the topic that support the students to know about the different method of finding the circumference of a circle.

icse syllabus 2013 is for all the respected classes according to their concern topics that helps the students in preparation of their exams and In the next session we will discuss about Asymptotes.