A one-to-one function is a type of mathematical function where each input (x-value) has a unique output (y-value). This means that no two different inputs can have the same output. It is also known as an injective function.
To determine if a function is one-to-one, you can use the horizontal line test. This involves drawing horizontal lines across the graph of the function. If the line intersects the graph at more than one point, the function is not one-to-one. If the line only intersects at one point, the function is one-to-one.
In a one-to-one function, the equation h(x,y)=x/(y+1) indicates that each input (x,y) will have a unique output. This is because the denominator (y+1) ensures that no two different inputs can have the same output. Therefore, this equation represents a one-to-one function.
No, by definition, a one-to-one function cannot have the same output for two different inputs. This means that each input must have a unique output in order for the function to be one-to-one.
The inverse of a one-to-one function is a function that reverses the input and output of the original function. In other words, the input of the original function becomes the output of the inverse function, and vice versa. This is denoted as f-1(x) and can be found by switching the x and y values in the original function and solving for y.