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Test for Functions (Summary)
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..
Infinite limits
Let f(x) be a function of x, if the value of f(x) can be made greater than any pre-assigned number by taking x close to 'a', then we say Similarly, if the value of f (x) can be made less than any pre-assigned number by taking x close to 'a', then we say f (x) tends to - as..
Let f(x) be a function of x, if the value of f(x) can be made greater than any pre-assigned number by taking x close to 'a', then we say Similarly, if the value of f (x) can be made less than any pre-assigned number by taking x close to 'a', then we say f (x) tends to - as..Many-one function
Every one element of A corresponds to more than one element of B. In example 3, one image has three pre-images. In example 4, one image has four pre-images. Therefore, many-one relations in examples 3 and 4 are many-one functions. Consider the following examples and note why th..
4. Into function
There is at least one element of B which has no pre-image. In above fig.(i) the function is one-one and into, while in fig.(ii) the function is many-one and into. For types of functions, the four arrow diagrams given for one-one and many-one are repeated for ONTO and INTO functions..
There is at least one element of B which has no pre-image. In above fig.(i) the function is one-one and into, while in fig.(ii) the function is many-one and into. For types of functions, the four arrow diagrams given for one-one and many-one are repeated for ONTO and INTO functions..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 has a corresp..
Function
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..
Function Solved Examples
The arrow diagram represents a relation from set A to set B. (i) Represent the relation in roster form. (ii) Is this relation a function? Give reason for your answer. (i) {(1, 2), (2, 4), (5, 2), (3, 10), (4, 10)} (ii) Yes it is a function. Every first element is mapped and it is m..
Key
n - neutron U - 235 Uranium Ba - Barium Kr - Krypton E - Energy Note : The number of neutrons released in a uncontrolled chain reaction of U-235 nuclei is given by 3 n where n = 1,2,3,..... A Schematic Diagram Showing Essential Steps in a Chain Reaction Based on Fission of U-2..
n - neutron U - 235 Uranium Ba - Barium Kr - Krypton E - Energy Note : The number of neutrons released in a uncontrolled chain reaction of U-235 nuclei is given by 3 n where n = 1,2,3,..... A Schematic Diagram Showing Essential Steps in a Chain Reaction Based on Fission of U-2..Key points
In a holiday mood - rest and recreation - made for the canal with a friend - pleasant weather - swam for an hour - felt hungry - returned home - had a light breakfast - read newspapers and India Today - had a chit-chat with a cousin - we lunched together - enjoyed a short nap -went to see a Matin..
Key Concepts
Diagonal relationship - It refers to the similarly in the properties of some of the elements of 2nd period to diagonally opposite elements of 3rd period. The pair of elements showing diagonal resemblance are: LiMg, Be..Al and B.S..
Result
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