# 3.2 - Function Notation Flashcards

I understand what a function is

A function is a mapping between two sets.

It takes some *input* numbers, and it produces *output* numbers

I can understand function notations of the form *f(x) =*

For example, *f(x) = 2x + 14* means…

*f* is a function which takes any number *x*, multiplies it by 2 and adds 14.

I can understand function notation of the form *f : x ↦ …*

For example, *f : x ↦ 3x + 2* means…

*f* is a function which takes any number *x*, multiplies it by 3 and adds 2.

I know what the domain of a function is

For example, the domain of the function: *f(x) = x<sup>2</sup>* is…

All positive numbers (because the output of *f* can never be negative).

I know what the range of a function is

For example, the range of the function: *f(x) = 1/(x - 1)* is…

All numbers *except* 1 (because if *x=1*, then *f(x)* involves a division by zero, which is impossible)

Can compose two functions *f* and *g*

For example, if *f(x) = x + 2* and *g(x) = 4x + 5*, then *fg(x) =* …

fg(x) = f(g(x)) = g(x) + 2 = (4x + 5) + 2 = 4x + 7

I can find the inverse function *f<sup>-1</sup>*

For example, if *f(x) = 7x - 2*, *f<sup>-1</sup>* is…

y = 7x - 2 y + 2 = 7x (y + 2)/7 = x

so

*f<sup>-1</sup>(x) = (x + 2)/7*