Finding all inverses Find all the inverses associated with the following functions, and state their domains.


ƒ(x) = 2 / ( x² + 2)

Key Concepts

Inverse Functions

An inverse function essentially reverses the effect of the original function. If a function f takes an input x and produces an output y, the inverse function f⁻¹ takes y back to x. For a function to have an inverse, it must be one-to-one, meaning each output is produced by exactly one input.

Domain and Range

The domain of a function is the set of all possible input values (x-values) that the function can accept, while the range is the set of all possible output values (y-values) that the function can produce. When finding the inverse of a function, the domain of the original function becomes the range of the inverse, and vice versa.

Finding Inverses Algebraically

To find the inverse of a function algebraically, you typically start by replacing f(x) with y, then swap x and y in the equation. After that, you solve for y to express it in terms of x. This new expression represents the inverse function, and it is important to also determine its domain based on the original function.