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The Manga Guide to Linear Algebra by Ltd. Trend-Pro Co., Iroha Inoue, Shin Takahashi

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40 Chapter 2 The Fundamentals
Next up are
images.
Images?
Let’s aume that
x
i
is an element of
the set
X.
The element in
Y that
coesponds to
x
i
when put through
f...
is caed “
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
Cuy
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
schl 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 with2
in this formula,
I'msuosed to write
f(2) and...
Actuay...
I have!
Inside
Misa’sbrain
?
Functions 43
We,
here’s
w hy.
What
f(x) = 2x − 1
reay means is this:
Oh!
So that's what
itmeant!
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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