Mathematical formulas

Differential Calculus

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Sections

1Notation, functions and domains
2Limits
3Continuity
4Derivative and geometric interpretation
5Differentiation rules
6Higher-order derivatives
7Mean value theorem
8Function analysis
9Optimization
10Linear approximations and differentials
11Taylor series (introduction)
12L'Hôpital and indeterminate limits
13Implicit and related functions
14Related rates
15Graphs and asymptotic behavior
16Guide to differentiate and analyze
AAppendix A: extended derivative table

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Differential Calculus
Composition and inverse
Formula

1.3. Composition and inverse

Formula

In 1.3. Composition and inverse

Formula

f(f^{-1}(y))=y,\qquad f^{-1}(f(x))=x

Tags

Differential calculus
Domain
Functions
Notation
Composition and inverse

Detail

Identities of a bijective function and its inverse on their respective domains.

Variables

$x$ Independent variable
$f$ Function
$y$ Dependent variable

Conditions

$f^{-1}(f(x))=x$

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$(f\circ g)(x)=f(g(x))$
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