We start by recalling the key concept: The inverse of a function. 
Definition INV Inverse Function

The elementary functions are defined initially from a list of core functions.

The definition continues with a recursive formulation, building more elementary functions from previously defined elementary functions by using arithmetic operations, composition of functions, and inverting functions.

In this section we link to previous subsections on visualizing the inverse of functions with mapping diagrams to make sense of elementary functions formed by inversion.

Visualizing inverses of functions with mapping diagrams is not a new concept.

It was covered first in the section on linear functions, specifically in Subsection LF.INV: Inverse of a Linear Function.

In fact, inverse functions have been discussed in almost every section of this resource!
You can review those subsections here:

QF.INV "Inverse" of a Quadratic Function

OW.ICPPF Inverse for Core Positive Power Functions

ELF.CELF Core Exponential and Logarithmic Functions

ELF.INV Inverses for Exponential and Logarithmic Functions

TRIG.INV Inverses for Trigonometric Functions