OEF inverse
--- Introduction ---

This module actually contains 6 exercises on the inverse function of a real bijective function: domain of definition, evaluation, derivative, etc.

Quadratic bijectivity

Consider the ``function'' : [,] -> [,] defined by

(x) = .

What is the nature of  ?

Fraction

Let : [,] -> [,] be the function defined by

(x) = .

Verify that is bijective, and compute the inverse function -1: [,] -> [,].

You may type sqrt(2) for the square root of 2 for example.

Inverse value

Let : -> be the function defined by

(x) = .

Verify that is bijective, therefore we have an inverse function -1: -> . Calculate the value -1().

You must reply with a pricision of at least 4 significant digits.

Non-differentiable inverse

The function : -> defined by

(x) = 

is bijective, but there is a point    such that the inverse function -1(x) is not differentiable on . Find .

Quadratic

Let : [,] -> [,] be the function defined by

(x) = .

Verify that is bijective, and compute the inverse function -1: [,] -> [,].

You may type sqrt(2) for the square root of 2 for example.

Inverse derivative

Let : -> be the function defined by

(x) = .

Verify that is bijective, therefore we have an inverse function (x) = -1(x). Calculate the value of derivative  '() .

You must reply with a pricision of at least 4 significant digits.

Other exercises on: inverse functions   functions  

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Description: collection of exercises on the inverse function of a real bijective function. This is the main site of WIMS (WWW Interactive Multipurpose Server): interactive exercises, online calculators and plotters, mathematical recreation and games

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