Inverted Functions
Inverted functions are mathematical functions that reverse the effect of the original function. If a function f takes an input x and produces an output y, the inverse function, denoted as f⁻¹, takes y back to x. This means that applying the inverse function to the output of the original function returns the original input.
To find the inverse of a function, you typically swap the roles of x and y in the equation and then solve for y. Not all functions have inverses; a function must be one-to-one, meaning it passes the horizontal line test, to ensure that each output corresponds to exactly one input.