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 …
Here you will learn algebraic operations on functions, equal or identical functions and homogeneous function. Let’s begin – Algebraic Operations on Functions Various operations, namely addition, subtraction, multiplication, division etc on real function are : (i) Addition : Let f : \(D_1\) \(\rightarrow\) R and g : \(D_2\) \(\rightarrow\) R be two real functions. Then, …
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 …
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) = …
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Here, you will learn what is a periodic function with definition and example. 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) = f(x), for …
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Here, you will learn one one and onto function (bijection) with definition and examples. Let’s begin – What is Bijection Function (One-One Onto Function) ? Definition : A function f : A \(\rightarrow\) B is a bijection if it is one-one as well as onto. In other words, a function f : A \(\rightarrow\) B …
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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, …
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. …
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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 …
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 …
