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..
Following are the test for Functions
(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..
(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..3. Onto function
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 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..One-one function
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..
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..Examples:
i) Because the element c A is not associated with an element of B. ii) Because the element a A has no unique association. Hence y = f(x), y is called the image of x and x is called the pre-image of..
i) Because the element c A is not associated with an element of B. ii) Because the element a A has no unique association. Hence y = f(x), y is called the image of x and x is called the pre-image of..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..
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 Solved Examples
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): ..
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): ..Algebraic identity
An algebraic identity is a statement of equality between two algebraic expressions, but it is satisfied for all values of the variabl..
..Equations
Fundamentals of Equations Algebraic and transcendental equations; If f(x) is a polynomial in x, then f(x) =0 is an algebraic equation. Example; x 7 + 5x - 2=0. If f(x) contains algebraic and non algebraic functions namely exponential, logarithmic, t..
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