Question

Mrs. Buttersworth

Answer 1

This is what I have so far
f(x) = 10x+5
x = 10y+5
-5 -5
what now?

Answer 2

@zimmah could you assist me a little?

Answer 3

i don't know part 3

Answer 4

i don't know how you can explain how something is a legitimate function

Answer 5

yeah that's kind of bothering me. I guess using it in a real life example?

Answer 6

oh, yes you could try that

Answer 7

I'm not exactly sure how I'd do that ._. I don't even have my function done

Answer 8

f(x) = 10x+5 is fine,

not sure what you was trying to do after that though

Answer 9

I'm supposed to solve it, I'm terrible at these kinds of things though. Apparently I'm supposed to "teach the martians" how to do functions.

Answer 10

let's say that function could describe the cost of a taxi per kilometer, and the +5 is the initial charge.

Answer 11

ye, that's just the flavor of the year apparently, i have seen that around a lot. They want to make math more 'exciting' by creating stories around it. It might work for some people.

I just think it's important to understand what you are doing, and how you can apply it

Answer 12

I think I might use that, that's kind of getting my mind going.
Alright and for the next question, I know you plug in 3 so it's like " f(3)= 10(3) + 5 "... but what next?

I mean, I get it's to prove it can be used for those who ask "when am I going to use this in my life" but there's also other equations that could solve the real life problems.

Answer 13

you can pretty much translate any problem into math problems. it doesn't even always have to do with numbers.

Answer 14

what do you mean with what's next?

Answer 15

you can just multiply the 3 and the 10 and add a 5 and you'll have the answer fo f(3), there's nothing left to do after that.

Answer 16

i mean you could pretend you had to explain it to your little sister (pretend you have one if you don't) if the 'explain in full sentences' is putting you off.

Answer 17

that's probably more exciting than to pretend telling it to martians. (even though in the off chance we do ever meet aliens, math is probably the way we could communicate with them in the first place, but that's a different subject altogether)

Answer 18

it's more interesting than math itself though xD
alright, if you don't mind, I'll see how much I can milk
could you help me find the inverse? c:

Answer 19

right, so in your function, if you put in 3, you get 35 as a result. so the inverse would be just the opposite (if you put in 35, you get 3 as a result)

Answer 20

to get from 3 to 35 you first multiplied with 10, and then added 5 (the order is important)

Answer 21

to get the inverse, we do the opposite operations in the opposite order

Answer 22

the opposite of adding 5 is subtracting 5

Answer 23

and then, the opposite of multiplying by 10 is dividing by 10

Answer 24

and to make sure it's correct, let's try (35-5)/10 =

the answer should be 3

Answer 25

the way they try teaching us is the whole (f(g(x)) way which gets kinda confusing if you aren't entirely focused when you learn it ._.
I wish I could just put the opposite o.e

Answer 26

i expected that one to come as well, it has been asked a lot the past week

Answer 27

f(g(x)) is pretty much the same as f(3) except instead of substituting all x's with 3's you now insert the whole function of g(x)

Answer 28

well, the next problem came to be h(x) instead, but none the less is equally confusing

"They ask you to create a new function, h(x). Then assign any number to x. Using complete sentences, explain whether f(h(x)) and h(f(x)) will always result in the same number. You will use the function f(x) that you created in problem number 2."

Answer 29

right, so like you made up a function for f(x), first you have to make up some h(x)

Answer 30

alright, what I'm thinking is

h(x)=15x-6?

Answer 31

Here's a little theory to clarify

A function is made up of several parts, here they are color coded.
\( \color{purple}{function} \)
\( \color{purple}{f(x)=10x+5}\)
\( \color{red}{name~of~the~function}\)
\(\color{blue}{variable~of~the~function}\)
\(\color{red}{f}(\color{blue}{x})=10\color{blue}{x}+5\)
\(\color{green}{argument~to~the~function~(replaces~variable)}\)
\(\color{red}{f}(\color{green}{5})=10\color{green}{(5)}+5\)
a more complex argument to the function (same principle applies)
\(\color{red}{f}(\color{green}{3x+4})=10\color{green}{(3x+4)}+5\)
using a function as argument to a function (again, same principle applies)
\( \color{purple}{h(x)=3x+4}\)
\(\color{red}{f}(\color{green}{h(x)})=10\color{green}{(3x+4)}+5\)

Answer 32

yes that will work

Answer 33

so, let's see what happens when you use h(x) as an argument to f(x)

so in other words, when you find the solution to f(h(x))

Answer 34

are you having problems with it?

Answer 35

sorry, I got busy

alright let's see what I can do

h(3) = 15(3)-6

h(3) = 45-6
39

and we know the other one is 35 so it'd be no.

Thank you Mister c:

Answer 36

no, that's not quite what they ask

Answer 37

they asked if the 2 were to always be the same, right? Resulting in the same number :o

Answer 38

they ask you to use the function h(x) as an argument to f(x) and vice versa, and see if it makes any difference. And than you should explain why there is a difference or why there is no difference.

Answer 39

yes but comparing f(h(x)) to h(f(x)) is not the same as comparing f(3) and h(3)

Answer 40

well, yeah but using any other number would also result in something different too :o

h(4) = 54 and f(4) would be 35 and so on :o

Answer 41

I think.. okay yeah, I didn't do f(h(x)) and h(f(x))

Answer 42

it's explained a bit in the colored text

Answer 43

so if h(3) = 39, would I use 39?

Answer 44

no

Answer 45

you use the complete function of h(x) and substitude the x's in f(x) with h(x)

Answer 46

sorry, the post showed before I submitted, so I'd use 15(3)-6?

Answer 47

yes, you use that as an argument to f(x)

Answer 48

so f(15(3)-6) = 10(15(3)-6)-5

Answer 49

and you compare that to h(f(3) which is

h(10(3)-5) = 15(10(3)-5)-6

Answer 50

dang it, you typed before me xD

Answer 51

sorry

Answer 52

it's okay xD

Answer 53

in fact it might be just as easy to just use x instead of 3, but i don't know what you think is easier

Answer 54

either way you can check to see if they get the same result or not, and you can try to come up with reasons why

Answer 55

3 was easier because I had something to plug in. Alright so the f(h(x)) gave me 385 and the h(f(x)) gave me 519, so either way it wouldn't work as being similar.

Answer 56

h(f(3)) = 369 actually, f(h(3)) = 385 indeed.

they are indeed not the same.

Do you know why?

Answer 57

I might have jumbled up somewhere

well, I know when 3 is plugged in, the results come out different so.. that's why?

Answer 58

not really, because both of them use both functions

Answer 59

you actually have all the same numbers and all the same operators

Answer 60

but still the result is different

Answer 61

hmm.. so any time I use a function similar, it'll most likely be different? or always different?

Answer 62

it's about the order of operations

Answer 63

even if you use the exact same numbers and the exact same operators, if the order is different, the outcome willchange

Answer 64

for example 3+2*7 is not the same as (3+2)*7