# Maths - Functions and Mappings

> Source: https://ollybritton.com/notes/a-level/maths/topics/functions-and-mappings/ · Updated: 2021-07-05 · Tags: maths, school

## Flashcards
##### What is the domain of a function??
The set of all possible inputs.

##### What is the range of a function??
The set of all possible outputs.

##### What is the range of a function sometimes called??
The codomain.

##### What is a mapping??
A transformation from one set of numbers into a different set of numbers.

##### When is a mapping a function??
When every input has a distinct output.

##### Other than a one-to-one function, what's another type of mapping that is also a function??
A many-to-one function.

##### How could you write the range of a function that has to be greater than $0$??
$$
f(x) \ge 0
$$

### 2021-07-07
##### Instead of solving $$f(x) = f^{-1}(x)$$ What can you solve instead??
$$
f(x) = x \\\\
f^{-1}(x) = x
$$

##### Instead of solving $$fg(x) = 7$$ What can you solve instead??
$$
g(x) = f^{-1}(x)
$$

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