actions are extremely important in mathematics as they serve as a window to all higher-dimensional in this discipline as well as models that most of applied mathematics available. Understanding this concept is essential to progress to higher levels. Here we discuss the specific characteristics of the active, to be one-on-one.
A function two parameters x and Y is correspondence colleagues every x unique Y . In high school algebra classes, students learn to apply vertical line test to determine whether a particular communication is operative or not. When the plot points of action, we obtain the graph. If the graph is such that no point along the curve vertical line can be drawn that the cuts dig in more than one place, then graph representative function. If the line does intersect the graph in more than one place, then the graph simply Relations between x and Y and not function.
For example, the relationship y = 3x , which represents a straight line, is a function. Naturally line is loop over him, so goes the vertical line test. Moreover, this action belongs other special category called one-on-one work . The formal definition for a one-on-one work is such that for each x value corresponds to at most one unique Y value. That is, it can not be a situation where the value x is churned into two Y value, as the relationship y = x ^ 2 . In this action, both negative and positive x values are sent to the same positive Y value, as the number of squares is this. Specifically, both x value 1 and -1 sent 1 .
It is enough for this to happen for one set x values to categories of work that not one-on-one. Another way to test for one-on-one ness using h orizontal line test. In line with the vertical test, this test tells us immediately whether the graph represents one-on-one work or not. If the horizontal line can be drawn at any point on the curve so that more than one group graph is cut twice , the graph makes not represent a one-on -Man function, as the parabolic y = x ^ 2 .
The concept of one-to-one function plays an important role in determining inverse function of a particular function. The inverse function really can be thought of as a function of undoes what the original function did. For example, if a function takes effect 3 and sent it to 6 , the inverse operation takes effect 6 and sent it back to 3 . Name action can only be obtained from one-on-one action
The concept of one-to-one and inverse function plays an important role in all sectors of higher mathematics and indeed analysis. but before you can run, you have to learn to walk, and these concepts clear the road so as to make smooth.