Math Tutoring on Determining Inverse Functions
If a function is defined so that each range element or y value is used only once then it is a One-to-one Function. If every y value is only paired with one x value we have a special type of function called a One-to-one Function and in math tutoring a Horizontal Line Test helps to determine graphically whether a function is one-to-one. If a horizontal line does not intersect the graph of a function in more than one point it is a One-to-one Function and what is so important about this is that only One-to-one Function have Inverse Functions. If f is a function from a set A to a set B, then an Inverse Function of ‘f’ is a function from B to A , with the property that a round trip or composition from A to B to A' ( or from B to A to B ) returns each element of the initial set to itself. Thus if an input x into the function f produces an output y, then in putting y into the inverse function produces the output x and vice versa.
f (g(x)) = g(f(x)) = x
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1. What is a one to one function?
2. How does one to one function be related to Inverse function?
3. What is meant by invertible?
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