3.2 - Function Notation

Question 1

I understand what a function is

Answer 1

A function is a mapping between two sets.

It takes some input numbers, and it produces output numbers

Question 2

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

For example, f(x) = 2x + 14 means…

Answer 2

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

Question 3

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

For example, f : x ↦ 3x + 2 means…

Answer 3

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

Question 4

I know what the domain of a function is

For example, the domain of the function: f(x) = x² is…

Answer 4

All positive numbers

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

Question 5

I know what the range of a function is

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

Answer 5

All numbers except 1

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

Question 6

Can compose two functions f and g

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

Answer 6

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

Question 7

I can find the inverse function f ^-1

For example, if f(x) = 7x - 2, f ^-1 is…

Answer 7

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

so

f ^-1(x) = (x + 2)/7