40 Chapter 2 The Fundamentals

Next up are

images.

Images?

Let’s aume that

x

i

is an element of

the set

X.

The element in

Y that

coesponds to

x

i

when put through

f...

is caed “

x

i

's image under f in Y.”

Also,

it's not uncoon

to write “

x

i

's image

under

f in Y”...

As

f(x

i

).

x

i

's image

under

f

in

Y

Okay!

Images

Functions 41

Yurino

Yoshida

Yajima

Tomiyama

Udon

Cuy

Breaded pork

Broiled l

f

X Y

And in our case...

Like this:

I hope you

like udon!

Image

This is the element in Y that corresponds to x

i

of the set X, when put through

the function f.

f (Yurino) = udon

f (Yoshida) = broiled l

f (Yajima) = breaded pork

f (Tomiyama) = breaded pork

42 Chapter 2 The Fundamentals

By the way, do you

remember this type of

formula from your high

schl years?

Oh...

yeah, sure.

Didn't you ever

wonder why...

...they always used

this weird symbol

f(x)

where they could have

used something much

simpler like y instead?

“Like whatever!

Anyways, so if I want

to substitute with2

in this formula,

I'msuosed to write

f(2) and...”

Actuay...

I have!

Inside

Misa’sbrain

?

Functions 43

We,

here’s

w hy.

What

f(x) = 2x − 1

reay means is this:

Oh!

So that's what

itmeant!

Similarly,

f(2) implies this:

I think I'm

starting to

get it.

So we were using

functions in high

schl t?

Exa ctly.

The function

f is a rule that says:

“The element x of the set X

goes together with the element

2x − 1 in the set Y.”

The image of 2 under the function f is 2 ∙ 2 − 1.

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