Math academic team coach trying to explain this to 8th graders... Answer is 1 but how

[deft ivy]

huh

fog isn't just used for functions?

how do you calculate fog with sets?

@flint shuttle what do you think

[flint shuttle]

(6,12) makes sense

Think of (x,y) pairs

[deft ivy]

but what does fog mean

with ensembles

sets

idk how it's called

[flint shuttle]

g(6) = 8 and f(g(6)) = f(8) = 12

[flint shuttle]

f o g = f(g(x))

[deft ivy]

yes i know

but that makes sense for functions

[flint shuttle]

it's a more general concept

f = { ... } refers to the set of points

(x,y) points

(x,y) are the elements of the set

f o g we are basically looking such x where g(x) is in the domain of f(x)

6 is such x because g(6) = 8

and f(8) is defined as 12

that's all

so f(g(6)) = 12 or (6,12)

[deft ivy]

oh alright

thanks

[flint shuttle]

https://en.wikipedia.org/wiki/Function_composition

hope OP understand too

[deft ivy]

OP?

[flint shuttle]

Original Poster*

[alpine fox]

$f\circ g={(x, z) :\exists y((x, y)\in f \wedge (y, z)\in g)}$

[coarse chasm]

SWR

[flint shuttle]

haha

like an 8-grader would understand this SWR

[alpine fox]

This is an 8th grade academic team. They need to step up

[flint shuttle]

what is that anyway

[alpine fox]

An after-school group of students who participate in math competitions against teams from other schools

[flint shuttle]

oh

[alpine fox]

@frosty fossil your students need to first understand sets and ordered pairs.

[flint shuttle]

i tried to explain it in my terms, you think it's ok?

[alpine fox]

This is kinda unclear to read. I get what you're saying, but it reads a little awkwardly

OP hasn't replied at all though, so I'm just gonna leave this post alone for now.

[frosty fossil]

ohhh so have them plug in f(g(x)) for 6 and that gives them an ordered pair? yeah that SWR won't work but I can explain compostition of functions to them just never had seen it with ordered pairs like that

I have another one that would be helpful...How would I go about teaching them lcm when they have 30-40 seconds to answer?

why is 4 the answer here

[thorn sparrow]

are you the coach or the student Logman

[deft ivy]

what does extraneous solution mean?

[frosty fossil]

I'm the coach

dividing by 0, I just want to know how these kiddos will be able to quickly find which roots will cause that besides drill and kill

but if drill and kill is the answer we'll do it lol

[deft ivy]

so?

[frosty fossil]

what?

[deft ivy]

what's an extraneous solution?

[frosty fossil]

Bruh. It's a solution that is not valid aka dividing by zero

is there a formula for finding it it these type of problems? I am trying to find a quick way for my students to solve these

@alpine fox any help you could throw this way would appreciated

[deft ivy]

I don't know the terms in english 💀

[deft ivy]

well all of them have extraneous solutions

they're not hard to find

[frosty fossil]

See that's what i'm confused about too! like doesn't #1 have extraneous solutions? but it says the answer is 2

and kids only get like 40 seconds to maybe a minute so simpliflying these needs to be quick

[deft ivy]

huh

no

[frosty fossil]

oh wait sorry no 4 is the answer

[deft ivy]

1. has -1/2 and -2, 2) has -3 and 3, 3) has 3 and 0 and 4) has 2 and -2

[frosty fossil]

how did you get those just setting each denominator to zero?

[deft ivy]

yes

[frosty fossil]

but it says 4 is the only one with extraneous solution...let me email the question creator

[alpine fox]

Fastest way I can think of doing it is checking what solutions could be extraneous, and then see if you get 0 in the numerator once you the denominators common

[deft ivy]

but here the equations are so fast to solve (denominator=0)

[alpine fox]

For example, problem 4: extraneous could be 2 or -2. I check if either are a solution to 4x²-2x(x+2)=1(x-2). -2 is not, but 2 is.

[frosty fossil]

.close