Write an equation for the inverse function of each one-to-one function given. ƒ(x) = 4^x+2

Key Concepts

One-to-One Functions

A one-to-one function is a type of function where each output is produced by exactly one input. This means that no two different inputs can yield the same output. Understanding this property is crucial for finding the inverse of a function, as only one-to-one functions have inverses that are also functions.

Inverse Functions

An inverse function essentially reverses the effect of the original function. If a function ƒ takes an input x and produces an output y, the inverse function ƒ⁻¹ takes y back to x. To find the inverse, we typically swap the roles of x and y in the equation and solve for y.

Exponential Functions

Exponential functions are functions of the form ƒ(x) = a^x, where a is a positive constant. They are characterized by their rapid growth or decay and are essential in various applications. To find the inverse of an exponential function, we often use logarithms, as they are the inverse operations of exponentiation.