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539Understanding Function Notation
540Evaluating Functions with Numeric Inputs
541Evaluating Functions with Variable Inputs
542Working with Multiple Functions
543Function Notation with Multiple Variables
544Solving Equations Involving Function Notation
545Evaluating Piecewise-Defined Functions
546Function Evaluation in Context
547Common Function Notation Mistakes
548What Are Domain and Range?
549Finding Domain from Equations
550Domain Restrictions from Square Roots
551Domain Restrictions from Rational Expressions
552Domain from Graphs
553Finding Range from Equations
554Range from Graphs
555Interval Notation for Domain and Range
556Domain and Range of Piecewise Functions
557Real-World Context and Restricted Domains
558Function Composition Basics
559Evaluating Composite Functions
560Domain of Composite Functions
561Decomposing Functions
562One-to-One Functions
563Finding Inverse Functions Algebraically
564Verifying Inverse Functions
565Graphs of Inverse Functions
566Domain and Range of Inverse Functions
567Inverses of Restricted Functions
568Compositions Involving Inverses
569Even and Odd Functions
570Periodic Functions
571Monotonicity: Increasing and Decreasing Functions
572Bounded Functions
573Extrema: Local and Absolute Maxima and Minima
574Average Rate of Change
575End Behavior and Limits at Infinity
576Continuity of Functions
577Zeros and Intercepts
578Vertical Shifts of Functions
579Horizontal Shifts of Functions
580Vertical Stretches and Compressions
581Horizontal Stretches and Compressions
582Reflections Across the x-axis
583Reflections Across the y-axis
584Combining Multiple Transformations
585Writing Transformed Functions from Descriptions
586Identifying Transformations from Equations
587Even and Odd Functions Under Transformation
588Transformations and Function Families
589Inverse Relationships in Transformations
590Definition and Notation of Piecewise Functions
591Evaluating Piecewise Functions
592Graphing Piecewise Functions
593Continuity of Piecewise Functions
594The Absolute Value Function
595The Greatest Integer (Floor) Function
596The Ceiling and Rounding Functions
597The Sign Function
598Writing Functions as Piecewise Definitions
599Applications of Piecewise Functions

539Understanding Function Notation
540Evaluating Functions with Numeric Inputs
541Evaluating Functions with Variable Inputs
542Working with Multiple Functions
543Function Notation with Multiple Variables
544Solving Equations Involving Function Notation
545Evaluating Piecewise-Defined Functions
546Function Evaluation in Context
547Common Function Notation Mistakes
548What Are Domain and Range?
549Finding Domain from Equations
550Domain Restrictions from Square Roots
551Domain Restrictions from Rational Expressions
552Domain from Graphs
553Finding Range from Equations
554Range from Graphs
555Interval Notation for Domain and Range
556Domain and Range of Piecewise Functions
557Real-World Context and Restricted Domains
558Function Composition Basics
559Evaluating Composite Functions
560Domain of Composite Functions
561Decomposing Functions
562One-to-One Functions
563Finding Inverse Functions Algebraically
564Verifying Inverse Functions
565Graphs of Inverse Functions
566Domain and Range of Inverse Functions
567Inverses of Restricted Functions
568Compositions Involving Inverses
569Even and Odd Functions
570Periodic Functions
571Monotonicity: Increasing and Decreasing Functions
572Bounded Functions
573Extrema: Local and Absolute Maxima and Minima
574Average Rate of Change
575End Behavior and Limits at Infinity
576Continuity of Functions
577Zeros and Intercepts
578Vertical Shifts of Functions
579Horizontal Shifts of Functions
580Vertical Stretches and Compressions
581Horizontal Stretches and Compressions
582Reflections Across the x-axis
583Reflections Across the y-axis
584Combining Multiple Transformations
585Writing Transformed Functions from Descriptions
586Identifying Transformations from Equations
587Even and Odd Functions Under Transformation
588Transformations and Function Families
589Inverse Relationships in Transformations
590Definition and Notation of Piecewise Functions
591Evaluating Piecewise Functions
592Graphing Piecewise Functions
593Continuity of Piecewise Functions
594The Absolute Value Function
595The Greatest Integer (Floor) Function
596The Ceiling and Rounding Functions
597The Sign Function
598Writing Functions as Piecewise Definitions
599Applications of Piecewise Functions

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Lesson 564 of 3,121·14. Functions in DepthPro lesson

Verifying Inverse Functions

Confirm two functions are inverses by showing f(f⁻¹(x)) = x and f⁻¹(f(x)) = x for all valid inputs.

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