True or False: For a one-to-one function, y = f(x),then x = F^-1(y). Explain your answer.
Please help.
True. For a one-to-one function, where each value of x corresponds to a unique value of y and vice versa, the inverse function can be defined. The inverse function is denoted as f^(-1)(y). It swaps the roles of x and y, so if y = f(x), then x = f^(-1)(y). The inverse function allows us to obtain the original value of x for a given value of y.
True. In a one-to-one function, each element in the domain corresponds to a unique element in the range, and vice versa. If we have a one-to-one function with the equation y = f(x), then to find the inverse function, we simply need to swap the roles of x and y, and solve for the new y.
To do this, follow these steps:
1. Start with the given equation: y = f(x).
2. Swap the positions of x and y: x = f^-1(y).
3. Solve the equation for f^-1(y) to find the inverse function.
By following these steps, we can determine that x = f^-1(y) holds true for a one-to-one function.