What is the method to determine if a function is one-to-one? The geometric method is to draw a horizontal line on the graph and check if it inters...
What is the method to determine if a function is one-to-one?
The geometric method is to draw a horizontal line on the graph and check if it intersects the function graph at only one point.
If the function is one-to-one, then a function g with domain Y and range X is called the inverse function of f if f(g(x)) = x for each x in Y and g(f(x)) = x for each x in X.
To determine the inverse function of a function, we need to check if the function is one-to-one, change the nomenclature to y, solve for x, change the variables x and y, and then change y to f-1(x) to obtain the inverse function.
The geometric method is to draw a horizontal line on the graph and check if it intersects the function graph at only one point.
If the function is one-to-one, then a function g with domain Y and range X is called the inverse function of f if f(g(x)) = x for each x in Y and g(f(x)) = x for each x in X.
To determine the inverse function of a function, we need to check if the function is one-to-one, change the nomenclature to y, solve for x, change the variables x and y, and then change y to f-1(x) to obtain the inverse function.
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Ed 
The method to determine if a function is one-to-one is to check if each element in the domain maps to a unique element in the range. One way to do this is by using the horizontal line test. If a horizontal line intersects the graph of the function at more than one point, then the function is not one-to-one. If the horizontal line intersects the graph at only one point for every horizontal line, then the function is one-to-one.
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