#someone pls explain what R-> R is to me in 'f:R -> R, f(x) = x^2'

99 messages · Page 1 of 1 (latest)

onyx abyss
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jacplus tb was talking about codomain and domain but didnt explain anything lol, pls help

brave archBOT
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onyx abyss
wild lava
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for the function

onyx abyss
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yeh iget what the domain is

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what does it mean by 'domain of f'

wild lava
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Well, exactly that

onyx abyss
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is it different to 'domain of f(x)'?

wild lava
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f(x) is not a function

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it is the output value of the function, when you give x as an input

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A function is like a microwave

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x is the food

onyx abyss
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from where ive been learning ive had questions like 'find the domain or range of f(x)'

wild lava
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f(x) is the warm food

onyx abyss
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ok i get that now

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tysm for dumbing it down that much 😭

wild lava
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But at this point most people don't bother to make the distinction

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For no valid reason.

onyx abyss
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hm aight thats pretty interesting

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ill keep that in mind

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so what would the colon inbetween f: R - > R mean then

wild lava
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It's just an indicator

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I guess similarly to the "notice" of a microwave

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don't put aluminium inside

onyx abyss
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ahhh

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and the arrow?

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thats the same as (R, R) right

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even though that wouldnt make sense

wild lava
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f : D -> R, is a function that takes inputs in D and provides outputs in R

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the arrow here is also standard notation

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for that "notice"

onyx abyss
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so if i did f : 3 -> A, then everything following from 3 comes out as A

wild lava
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3 is not a set

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You can think of this example, f : R -> {-1, 0, 1}

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R is the set of real numbers

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and {-1, 0, 1} is a set that contains the three elements -1, 0 and 1

onyx abyss
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so R -> {-1, 0, 1} from my own understanding, is trying to say there can be any real numbers inbetween the set of {-1, 0, 1}

wild lava
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no

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f : R -> {-1, 0, 1}

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it means that you have a function f

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that takes input values x in R

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and you know for sure

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that f(x) is either -1, 0 or 1

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according to this notice, it cannot be anything else

onyx abyss
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I SEE NOW

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I GET IT

wild lava
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👍

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so here's another example

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f : {3} -> R

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is a function that can take nothing but 3 as an input

onyx abyss
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R -> {-1, 0, 1} means it takes nothing but {-1, 0, 1} as the input

wild lava
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the input can be any real number in R

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the source of the arrow indicates the input set

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and the end of the arrow indicates the output set

onyx abyss
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okay

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okay

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okay

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my eyes are being opened

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so if in the set or R,

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we input for say 2

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nothing will happen

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because the outputs are limited to -1, 0 and 1

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if what i said is right then i completely get it

wild lava
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Well, yes indeed

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f(2) will be either -1, 0 or 1

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if f : R -> {-1, 0, 1}

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on the other hand, for g : {3} -> R

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you CANNOT feed 2 to g

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it's like putting a banana in a microwave, when they explicitly tell you that you can only put cooked dishes

onyx abyss
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OKAY

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F : R -> R IS BASICALLY F(R) = R THEN NO?

wild lava
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That's another notation

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but also no, not necessarily

onyx abyss
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how so?

wild lava
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for instance, let $f : \mathbb{R} \rightarrow \mathbb{R}$ defined by the relation: for any $x \in \mathbb{R}$, $$f(x) = x^2$$

kindred cedarBOT
wild lava
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Here, it is clear that for any $x \in \mathbb{R}, f(x) \geq 0$

kindred cedarBOT
wild lava
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However, for a subset $A$ of $\mathbb{R}$, we define:
$$f[A] = { f(x) | x \in A}$$

kindred cedarBOT
wild lava
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In particular, $f[\mathbb{R}]$ does not contain negative numbers

kindred cedarBOT
onyx abyss
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im sorry thats a bit too advanced for what im up to currently

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so i dont really get that

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but i understand the two notations are separate

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and i think thats all ill need to know for now mostly

wild lava
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for f : R -> R

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you know in advance that f takes inputs in R

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and any output will be in R

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but you don't know if R is the smallest set of outputs yet

onyx abyss
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okay

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yea i get the f: R -> R part now

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thats