# 3.2 - Function Notation Flashcards

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1
Q

I understand what a function is

A

A function is a mapping between two sets.

It takes some input numbers, and it produces output numbers

2
Q

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

For example, f(x) = 2x + 14 means…

A

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

3
Q

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

For example, f : x ↦ 3x + 2 means…

A

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

4
Q

I know what the domain of a function is

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

A

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

5
Q

I know what the range of a function is

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

A

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

6
Q

Can compose two functions f and g

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

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

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

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

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

so

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