Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Inverse Functions: Guided Exercises

In course

MATH-203(b): Analysis III

Le cours étudie les concepts fondamentaux de l'analyse vectorielle et l'analyse de Fourier en vue de leur utilisation pour résoudre des problèmes pluridisciplinaires d'ingénierie scientifique. ...

Description

This lecture covers the concept of inverse functions, focusing on guided exercises related to the inversion formula and the composition of functions. The slides provide step-by-step examples and solutions for finding inverse functions and understanding the properties of these functions.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructors (2)

Maria Colombo

David Valentin Strütt

Official source

Related concepts (32)

Inverse function

In mathematics, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by For a function , its inverse admits an explicit description: it sends each element to the unique element such that f(x) = y. As an example, consider the real-valued function of a real variable given by f(x) = 5x − 7. One can think of f as the function which multiplies its input by 5 then subtracts 7 from the result.

Function composition

In mathematics, function composition is an operation ∘ that takes two functions f and g, and produces a function h = g ∘ f such that h(x) = g(f(x)). In this operation, the function g is applied to the result of applying the function f to x. That is, the functions f : X → Y and g : Y → Z are composed to yield a function that maps x in domain X to g(f(x)) in codomain Z. Intuitively, if z is a function of y, and y is a function of x, then z is a function of x.

Function (mathematics)

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a function of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity).

Even and odd functions

In mathematics, even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses. They are important in many areas of mathematical analysis, especially the theory of power series and Fourier series. They are named for the parity of the powers of the power functions which satisfy each condition: the function is an even function if n is an even integer, and it is an odd function if n is an odd integer.

Composition of relations

In the mathematics of binary relations, the composition of relations is the forming of a new binary relation R; S from two given binary relations R and S. In the calculus of relations, the composition of relations is called relative multiplication, and its result is called a relative product. Function composition is the special case of composition of relations where all relations involved are functions. The word uncle indicates a compound relation: for a person to be an uncle, he must be the brother of a parent.

Related lectures (36)

Derivatives of Trigonometric Inverse Functions MOOC: Trigonometric, Logarithmic and Exponential Functions

Explores derivatives of trigonometric inverse functions and their properties, with examples and solutions included.

Algebraic Identities and Trigonometry

Covers algebraic identities, trigonometry, and real functions, including injective, surjective, bijective, and reciprocal functions.

Real Functions: Definitions and Properties

Covers real functions' definitions, properties, periodicity, and reciprocity, including maximum, minimum, and composition of functions.

Continuous Functions on Open Intervals MOOC: Analysis I MOOC: Analysis I (part 4) : Limit of a function, continuous functions

Explores continuous functions on open intervals and elementary functions constructed from algebraic functions.

Model Extension and Composition of Functions