definition 7.14 Inverse function

open in the book · parts/02-mathematical-methods/05-real-analysis.tex:198 · p. 205

ground object -- no derivation owed

Rests on

depends_on definition 7.13 Composite function ¶
- depends_on definition 7.9 Real function ¶
  - depends_on definition 3.43 Map ¶
    - depends_on definition 3.24 Quantifiers ¶
      - depends_on definition 3.23 Predicate ¶
    - depends_on definition 3.28 Set ¶
depends_on definition 3.47 Bijective map ¶

Supports

depends_on proposition 7.32 Derivative of the inverse function ¶
- depends_on definition 9.140 Amplitude and the Jacobi elliptic functions ¶
  - depends_on proposition 9.143 A cubic quadrature between two turning points ¶
  - depends_on proposition 9.141 First properties ¶
    - depends_on proposition 9.143 A cubic quadrature between two turning points ¶ ↺
    - depends_on proposition 9.142 The differential equation of the sine amplitude ¶
  - depends_on proposition 9.144 The pendulum equation at finite amplitude ¶
- depends_on proposition 7.61 The logarithm ¶
  - depends_on corollary 7.69 $\ee$ is the unique self-reproducing base ¶
    - depends_on remark 7.70 What the condition says ¶
  - depends_on definition 7.62 Real powers ¶
    - depends_on definition 7.90 The golden ratio ¶
      - depends_on proposition 7.91 The golden ratio ¶
    - depends_on proposition 7.63 Laws of real powers ¶
      - depends_on definition 7.90 The golden ratio ¶ ↺
      - depends_on lemma 7.67 The limit over real exponents ¶
      - depends_on proposition 7.68 The natural base ¶
      - depends_on proposition 7.91 The golden ratio ¶ ↺
      - depends_on proposition 7.89 Irrationality of square roots ¶
    - depends_on proposition 7.89 Irrationality of square roots ¶ ↺
  - depends_on lemma 7.67 The limit over real exponents ¶ ↺
  - depends_on proposition 7.68 The natural base ¶ ↺
  - depends_on proposition 7.63 Laws of real powers ¶ ↺
- depends_on proposition 9.141 First properties ¶ ↺
- depends_on proposition 9.19 Separation of variables ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Composite function	declared	parts/02-mathematical-methods/05-real-analysis.tex:205
`depends_on`	→	Bijective map	declared	parts/02-mathematical-methods/05-real-analysis.tex:205
`depends_on`	←	Derivative of the inverse function	declared	parts/02-mathematical-methods/05-real-analysis.tex:625