## FUNCTION SHORTCUT TRICKS

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## Introduction:-

Today, we will discuss In this section, you will get the Basic Concepts, Shortcut tricks, MCQ, and Explanations. you know shortcut tricks help us to solve the questions within few seconds.

Now you are going to know what is Function, Domain, Range, periodic function, Inverse of a function, and tyes of function.

## Function

Let A and B be two given sets then a mapping or special case of relation from A to B for which each element a Є A is associated with a unique element b Є B under the rule f, then this relation is called Function.

Here, b is known as image of a and a is known as pre-image of b under the mapping f.

If f is a function from A to B then we write f: A → B, set A is known domain of the function and the set B is known as Co-domain of the function f.

The set of all f- images of the elements of A is called the range of the function f.

## Domain

To know about how to find domain of a function with in few seconds click on the link below, where you will get lots of shortcut tricks to find domain of a function with shortcut tricks.

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## Range

In most of the competition exams, the question of the range of a Rational function always occurs.

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## Periodic Function

A function is said to be a periodic function if its each value is repeated after a definite interval. So a function f(x) will be periodic if a positive real number “T” exist such that, f(x+T) = f(x), for all x Є domain .

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## Inverse of a Function

If f: A → B be a bijection function (one one and onto), then the mapping f-1 : A → B which associates each b Є B with element a Є A such that f(a) = b, is called the inverse of the function f: A → B.

f-1: A → B, f-1  (b)= a it means f(a) = b.

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## Types of Function

One- one Function:- The function f: A → B is known as one – one function, if different elements of A have different images in B, i.e two different elements in A do not have the same image in B. it is also known as an injective function.

Onto Function:- The function f: A → B is known as onto function if every element of B has at least one pre-image in A. it is also known as a surjective function.

Into Function:- The function f: A → B is known as into function if there exists at least one element in B which has no pre-image in A.

Many one Function:- The function f: A → B is known as many one function if two different elements in A have the same image in B.

Note:- if a function is one-one and onto then it is known as a bijective function.

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## Nitin Sharma Maths

#### Functions Test Series (MCQ) BY- Nitin Sharma

Firstly Check Your Score with yourself and Then get Correct Answers with Shortcut Tricks

Q.5 If A contains 3 elements and B contains 4 elements, then the number of all one-one functions defined from A to B is

• (a )144
• (b )12
• (c) 24
• (d) 64

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## Conclusion

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