Logarithmic Function
The functions of the form y= log b x where b > 0 and b ≠ 1 is known as logarithmic functions. It should be noted that y= log b x is the inverse function of y=b x where b > 0 and b ≠ 1. And in particular when b = e. Since the exponential func..
The functions of the form y= log b x where b > 0 and b ≠ 1 is known as logarithmic functions. It should be noted that y= log b x is the inverse function of y=b x where b > 0 and b ≠ 1. And in particular when b = e. Since the exponential func..Relations and Functions
A relation R is a non-empty sub-set of a cartesian product. A relation is a set of ordered pairs, i.e., R A x B where A and B are two non-empty sets. Domain of a relation is the set of all first components. Range of a relation is the set of all second components..
Odd function
A function f : A B is said to be an odd function if f(x) = - f(-x) for all x A The domain and range of f depends on the definition of the function. Examples of odd function are y = sinx, y = x 3 , y = ta..
A function f : A B is said to be an odd function if f(x) = - f(-x) for all x A The domain and range of f depends on the definition of the function. Examples of odd function are y = sinx, y = x 3 , y = ta..Constant function
A function f : A B Such that A, B R, is said to be a constant function if there exist K B such that f(x) = k. Domain = A Range = {k} The graph of this function is a line or line segment parallel to x-axis. Note that, if k>0, the graph B is above ..
A function f : A B Such that A, B R, is said to be a constant function if there exist K B such that f(x) = k. Domain = A Range = {k} The graph of this function is a line or line segment parallel to x-axis. Note that, if k>0, the graph B is above ..Smallest integer function (Ceiling function)
For a real number x, we denote by [x], the smallest integer greater than or equal to x. For example, [5 . 2] = 6, [-5 . 2] = -5, etc. The function f:R R defined by f(x) = [x], x R is called the smallest integer function or the ceiling function. Domain: R Ran..
For a real number x, we denote by [x], the smallest integer greater than or equal to x. For example, [5 . 2] = 6, [-5 . 2] = -5, etc. The function f:R R defined by f(x) = [x], x R is called the smallest integer function or the ceiling function. Domain: R Ran..Determine whether the relation represented by the set of ordered pairs..
Determine whether the relation represented by the set of ordered pairs below is a function. Give the domain and range if it is a function. (2, - 4), (5, - 4), (- 6, - 4), (2, 4). => It is a function, domain: 2, 6, 5 and 2, range: 4 and 4 or It is a ..
Determine whether the relation is a function or not.
Determine whether the relation is a function or not. => It is a function. or It is not a function. or It is a function with same domain and range. or cannot be determined..
Derivative of Inverse Trignometric Functions
Derivative of Inverse Trignometric Functions - Before finding the differentiation of inverse trigonometric functions, recall how the inverse trigonometric functions are defined and what the domain and range of each inverse trigonometric function. Fo..
Derivative of Inverse Trignometric Functions - Before finding the differentiation of inverse trigonometric functions, recall how the inverse trigonometric functions are defined and what the domain and range of each inverse trigonometric function. Fo..Functions, Limits and Continuity
Conclusion - In this chapter, we have studied various types of functions and their graphs. The use of graphs also facilitate the study of domain and range of functions..
Types of Functions Mapping
Functions - Let A and B be two non-empty sets.Let A and B be two non-empty sets. A function f from A to B is an association of every element of A to an unique element in B. We write this as f : A g B. A is called the domain. B is called the co-domain..
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