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In general the function and it inverse are not the same and do not have the same graph. If we look at a special function f(x)=x, it is equal to its inverse and the graph is the same. Think of the inverse of a function as changing all the x's to y's and vice versa. Well, in the function f(x)=x, all the x's are already y's and vice versa so it is its own invese.
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Is the inverse of the function y x2 still a function?
Y = 1/X2 ==============Can it pass the line test? * * * * * That is not the inverse, but the reciprocal. Not the same thing! The inverse is y = sqrt(x). Onless the range is resticted, the mapping is one-to-many and so not a function.
Is graph and chart similar?
In statistics, a graph and a chart are the same. In arithmetic, a graph is the plot of a function over values. There are no charts.
Why it is valid to say that both a function and its inverse describe the same relationship.?
If a function has an inverse then it is a bijection between two sets. Each element in the first set is mapped to one, and only one, element of the second set. Therefore, for each element in the second set there is one, and only one, element in the first set. The function and its inverse, both define the relationship between the same pairs of elements.
What test determines if a function is one to one?
First recall that a function is one to one if no two elements in its domain have the same element in the range One trick to finding out if a function is one to one is to use the Horizontal line test. You may view the link for a better explanation. The main idea is if a horizontal line intersects the graph of a function more than one time, then the function is not one to one. This is important because if it is not one to one, it has no inverse.
What does function of x equals function of -x mean?
It means that the value of the function at any point "x" is the same as the value of the function at the negative of "x". The graph of the function is thus symmetrical around the y-axis. Examples of such functions are the absolute value, the cosine function, and the function defined by y = x2.
