Finding inverses Find the inverse function.


ƒ(x) = 3x - 4

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 as input and returns x. For a function to have an inverse, it must be one-to-one, meaning each output is produced by exactly one input.

Algebraic Manipulation

Algebraic manipulation involves rearranging equations to isolate variables. To find the inverse of a function, you typically start by replacing f(x) with y, then solve for x in terms of y. This process often requires skills such as adding, subtracting, multiplying, and dividing both sides of the equation.

Function Notation

Function notation is a way to denote functions and their outputs clearly. In this context, f(x) represents the output of the function for a given input x. Understanding function notation is crucial for identifying the original function and correctly expressing its inverse, typically denoted as f⁻¹(x).