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The relation should be one-one or many-one, and Every first element is mapped which means that every pre-image should have an imag..

Before describing the limits of trigonometric functions, we state few theorems along with Sandwich theorem, which helps in calculating a variety of limits in subsequent chapter..

Every element of the set B has at least one pre-image. In above fig.(i), the function is one-one and onto, while in fig.(ii) the function is many-one and on..

Every one element of A corresponds to one element of B. Every first element has a corresponding second element. One-one relations in examples 1 and 2 are called one-one functions. Every element of set A has one image in set B. {(1, 4), (2, 4), (3, 4), (4, 5)} Here, one image has three pre..

In algebra we come across certain products very frequently. For e.g., (a + b) 2 , (a + b) 3 (a + b + c) 2 etc. These are nothing but products of binomials or trinomials. We derive the formulae for these products and apply them whenever necessary. These expansions help us to avoid elab..

(a) (i) The relation should be one-one or many-one, and (ii) Every first element is mapped which means that every pre-image should have an image. (b) For graphs: Draw a line parallel to the y-axis. If it cuts the graph only in one point, then the graph represents a function. If it cuts i..

Function - Any relation on A x B in which (i) no two second elements have a common first element and (ii) every first element has a corresponding second element is called a function.Any relation on A x B in which (i) no two second elements have a common first element and (ii) every first element ha..

Reasons: (i) (0, 5), (0, 1) pairs make it one - many, one - many is not a function. (ii) Pre-image 2 does not have an image in B. It becomes easy to discuss a function with the help of an arrow diagram. Given A = {-2, -1, 0, 1, 2} and B = {-3, -1, 1, 5}. list the elements of S = {(x, y): ..

An algebraic identity is a statement of equality between two algebraic expressions, but it is satisfied for all values of the variabl..

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