The inverse of a function is a function that undoes the original function. It swaps the input and output values of the original function, essentially performing the reverse operation.
To find the inverse of a function, you can follow these steps:
1. Write the original function in the form y = f(x).
2. Swap the x and y variables.
3. Solve for y to get the inverse function, which will be in the form x = f^-1(y).
The notation for an inverse function is f^-1(x), where the "^-1" represents the inverse.
To graph an inverse function, you can use the reflection method. Draw the original function on a coordinate plane, then reflect it over the line y = x. The resulting graph will be the inverse function.
No, not every function has an inverse. A function must be one-to-one (each input maps to a unique output) in order to have an inverse. If a function is not one-to-one, it will not have a unique inverse.