Composite and inverse functions

Apply functions in order and check when the reversed correspondence is a function.

Meaning

Composition uses one function's output as another's input. An inverse exists when reversing inputs and outputs again gives a function; restricting the original domain may be necessary.

Example

If and then The inverse returns output 5 to input 2.f first doubles an input and then adds 1. Undo the last operation first: subtract 1 from the output, then divide by 2. Different inputs give different outputs here, so reversing the correspondence is a function.In composition, an output must belong to the next domain. denotes an inverse function, not the reciprocal

Practice for this concept

Scope and references

Topics

Applying functions in sequence, reversing inputs and outputs, conditions for inverses

Learning goal

Apply functions in order and check when the reversed correspondence is a function.

Helpful background

Check domains and input–output correspondences.

Composition and inverses

These ordinary choice questions provide limited practice in this concept. They do not establish independent solution, full-concept performance, or mastery.

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