Why am I so fucking stupid and can't understand Functions in Algebra yet have gotten A's in all the classes and...

Why am I so fucking stupid and can't understand Functions in Algebra yet have gotten A's in all the classes and understand everything else? I'm basically asking why I can't understand them and what I can do better to do that... Not even my high school teachers were able to help me, let alone college professors.

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youtube.com/watch?v=_6B2PUn99Bc
en.wikipedia.org/wiki/Function_(mathematics)#Definition
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Functions are basically an assignment rule. What exactly is giving you trouble?

Well I understand basic functions since you just have to do substitutions, but once you start adding g(x) to it, it becomes confusing.

G(x) just means the assignment rule G applied to the object x.
Do you have a specific problem?

f(x) is essentially y.

Don't worry OP, not even mathematicians understand functions

youtube.com/watch?v=_6B2PUn99Bc

So you just plug in what g(x) equals into the x for f(x)?

Things like f(g(x)) mean first apply g to x, then apply f to the output...
Is any of this actually an algebra question?

you have to variables most of the times x and y
and then you define one variable about the other variable
>y=x^2
if u plug in many x you can draw a graph


>f(x) = x^2
is just another version of the same thing

An example to clarify:
F(x)=x^2,
G(x)=x+1,
Then
F(G(x))=(x+1)^2,
G(F(x))=(x^2)+1

>but once you start adding g(x) to it, it becomes confusing.

It's not confusing. You aren't studying and working enough problems or you are making excuses for yourself.

>Precalc threads get 10+ replies in under 5 minutes full of pedantic 15 year olds eager to prove how intelligent they are

Kill yourselves holy fuck.

>look at my edges
>still posting

How does he not know the usual definition of a function?

g(x) just means an expression whose only possible variable is x.

g(x) could be:

13x - 5
x + x^2
7

Just like h(x, y) can be:
cos(x) + 5y
2x
y^7 - 2y
4

and so on.

Your "usual definition" is probably incorrect.

Given an input, the function maps to exactly one value. That is to say, f(x) represents a transformation on the input of x. X can also be another function, lets say g(z). f(g(z)) is the value of z being mapped by the function g being mapped by the function f. Here is a simple example:

f(x) = x^2 // returns the square of the input
g(z) = z + 5 // takes the input and returns z+5

let z = 3 and be mapped by the compound function f(g(z)).
since f requires the input g(3), we can ignore it initially. g(3) = 3 + 5 = 8
Substitute 8 in f(g(z)) = f(8) = 8^2 = 64
Thus f(g(3)) = 8

A note here, since g of z is a value, it can replace every X in f(x).
So f(g(z)) = (z+5)^2.
You should note that letting z = 3 yields 64 just the same.

All you should take away is that a function is merely the transformation of one discrete value to another.

Haha you're a fucking nerd why would you put so much effort into attempting to educate a fucking underage on Veeky Forums of all places? Do you feel smart now?

The quality of the OP is what is killing the board and the more retards like you reply to this shit, the more they post their idiotic off-handeds

There's a reason Wildberger says that definition is wrong, and it's because it's not rigorous. He's right, but we fixed this a long time ago.

en.wikipedia.org/wiki/Function_(mathematics)#Definition

top kek and true

It's just a question of practice... do enough of it, it will stick.

-I had once met this teacher in grade 7, she was from Iraq and had taught University courses in England, however after the war had broken out (Op Freedom) she had fled to Canada, and (from what I understood) she had left her papers in Iraq. She was also an Architect.

Nevertheless, she liked me a lot and taught me a lot of math. I considered myself stupid when it came to understanding speed[born in raised in a very competitive culture, so if anyone beat me i consider myself slow and dumb... just the way i hold my standards]; however, she told me that in Arabic math is "ryadeeyat", which is translated to exercises. She said do enough of it you will master it.

She was right.

And you'd be the smug fuck in the back of the class who doesn't ask questions because he "already knows all the answers".

Enjoy your perfectionist lifestyle.