# Function

## Function Examples

Here you will learn some function examples for better understanding of function concepts. Example 1 : Find the range of the given function $$log_{\sqrt{2}}(2-log_2(16sin^2x+1))$$ Solution : Now 1 $$\le$$ $$16sin^2x$$ + 1) $$\le$$ 17 $$\therefore$$   0 $$\le$$ $$log_2(16sin^2x+1)$$ $$\le$$ $$log_217$$ $$\therefore$$   2 – $$log_217$$ $$\le$$ 2 – $$log_2(16sin^2x+1)$$ $$\le$$ 2 Now consider 0 …

## Algebraic Operations on Functions | Identical Function

Here you will learn algebraic operations on functions, equal or identical functions and homogeneous function. Let’s begin – Algebraic Operations on Functions If f & g are real valued functions of x with domain set A, B respectively, f + g, f – g, (f.g) & (f/g) as follows : (a) (f $$\pm$$ g)(x) = …

## Types of Functions in Maths – Domain & Range

Here you will learn types of functions in maths i.e polynomial function, logarithmic function etc and their domain and range. Let’s begin – Types of Functions in Maths (a) Polynomial function If a function is defined by f(x) = $$a_0x^n$$ + $$a_1x^{n-1}$$ + $$a_2x^{n-2}$$ + ….. + $$a_{n-1}x$$ + $$a_n$$ where n is a non …

## What is Inverse of a Function – Properties & Example

Here, you will learn what is inverse of a function, its properties and how to find the inverse of a function. Let’s begin – Inverse of a Function Let f : A $$\rightarrow$$ B be a one-one & onto function, then there exists a unique function g : B $$\rightarrow$$ A such that f(x) = …

## What is a Periodic Function – Definition & Example

Here, you will learn what is a periodic function with definition and example and composite function. Let’s begin – Periodic Function A function f(x) is called periodic if there exist a positive number T (T > 0), where T is the smallest such value called the period of the function such that f(x + T) …

## One to One Function and Onto Function – Many One & Into

Here, you will learn one to one function and onto functions, many one and into with example. Let’s begin – One to One (Injective mapping) A function f : A $$\rightarrow$$ B is said to be one to one or injective mapping if different elements of A have different f images in B. Thus there …

## Domain and Range of Greatest Integer Function

Here, you will learn domain and range of greatest integer function and properties of greatest integer function with example. Let’s begin – Greatest Integer Function or Floor Function For any real number x, we use the symbol [x] or $$\lfloor x \rfloor$$ to denote the greatest integer less than or equal to x. For example, …

## What is the Domain and Range of Modulus Function

Here, you will learn modulus function and what is the domain and range of modulus function. Let’s begin – The function f(x) defined by y = |x| = $$\begin{cases} x & \text{if}\ x \ge 0 \\ -x & \text{if}\ x < 0 \end{cases}$$ is called the modulus function. It is also called absolute value function. …

## How to Determine Odd Even Function

Here, you will learn what is odd even functions and how to determine if given function is odd or even with example. Let’s begin – Odd Even Function : Let a function f(x) such that both x and -x are in its domain then If f(-x) = f(x) then f is said to be an …

## How to Find Domain and Range of Function

Here you will learn what is domain, codomain and range of function and how to find domain and range of function with example. Let’s begin – Let f : A $$\rightarrow$$ B is a function. Then, the set A is known as the domain of f and the set B is known as the codomain …