online math pre algebra test

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..

A function f : A g B is called a 1-1 mapping, if every element of f(A) does not have more than one pre-image. ..

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..

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 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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The product of a + b and a 2 - ab + b 2 is a 3 + b 3 . Hence when a 3 + b 3 is factorised, we get: a 3 + b 3 = (a + b) (a 2 - ab + b 2 ) Similarly, a 3 - b 3 = (a - b) (a 2 + ab + b 2 ) Factorise: x 3 + 8 x 3 + 8 = (x) 3 + (2) 3 = (x + 2) (x 2 - 2x + 4) Factorise 64x 3 - 125. ..