A one-to-one function is a type of mathematical function where each input has exactly one corresponding output. This means that no two inputs will have the same output. In other words, each input has a unique output.
To determine if a function is one-to-one, you can use the horizontal line test. Draw a horizontal line across the graph of the function. If the line intersects the graph in more than one point, then the function is not one-to-one. If the line only intersects the graph at one point, then the function is one-to-one.
An inverse function is a function that "undoes" the original function. It is the reverse operation of the original function. In other words, if you input the output of the original function into the inverse function, you will get the original input value back.
To find the inverse of a one-to-one function, you can switch the positions of the input and output variables and solve for the new output variable. This new function will be the inverse of the original function. It is also important to note that the domain and range of the original function will be switched in the inverse function.
No, a function can only have one inverse. This is because the inverse function must "undo" the original function, and if there are multiple possible outputs for a given input, the inverse function would not be able to determine which input to return. In other words, a function can only have one inverse that satisfies the definition of an inverse function.