Question

The Martians ask you to explain one last thing, Ultimate Math Ambassador. Assign any number to x. Using complete sentences, explain whether f(g(x)) and g(f(x)) will always result in the same number. You will use the inverse function that you created in problem number 5 for g(x).

Answer 1

My inverse function -
x-6
------ = f(x)
10

I was learning it off of - http://openstudy.com/study#/updates/52331ea2e4b0af32a07890c2

Answer 2

@E.ali This is what I needed help on!

Answer 3

@Yttrium Would ya help me out?

Answer 4

you're not @Brad1996 eh ?

Answer 5

@ganeshie8 No, i was learning off of his question though

Answer 6

okie nice :)

Answer 7

@ganeshie8 Thanks, I'm just really confused, I would like if you solved it step by step and showed me in details how you did it.. I don't understand this at all and I'm falling behind due to it

Answer 8

okay lets do it...

read the question quickly,
and can u write down the f(x) and g(x) ?

Answer 9

@ganeshie8

f(x) = 10x+ 6

g(x) = (x-6)/10

if I remember correctly.

Answer 10

Awesome ! yes they're the two functions, which are inverses of eachother

Answer 11

next,
Assign any number to x.

Answer 12

wats ur fac number ? :)

Answer 13

*fav number

Answer 14

I'll choose the number 2. lol

Answer 15

very smart :) cuz 2 is small ha

Answer 16

ok, x = 2

Answer 17

next,

Using complete sentences, explain whether f(g(x)) and g(f(x)) will always result in the same number.

Answer 18

to do this, we need to calculate two things :-

f(g(2))

and

g(f(2))

Answer 19

Hmm alright, and how would we do that?

Answer 20

lets do f(g(2)) first

f(g(2))
^

Answer 21

do u see g(2) is inside, so we need to calculate it first

Answer 22

g(2) = ?

Answer 23

Well, I'm assuming we would multiply them which would be since there doesn't seem to be much else you can do.

Answer 24

i see wat u did there, but here \(g\) is not a variabel, \(g\) is a function !!!!

\(\large g(x) = \frac{x-6}{10}\)

Answer 25

so,

\(\large g(2) = \frac{2-6}{10}\)

Answer 26

simplify,

Answer 27

above, basically, to get g(2), we just replaced x wid 2

Answer 28

Simplified would be g(2) = -2/5

Answer 29

Really bad computer drawing ability, lol.

Answer 30

that looks good, sorry, i gtg
but il be back in 20 mibutes

Answer 31

Okay, I'll work on another class while I'm waiting. :)

Answer 32

m back @Smores

Answer 33

u still here ? :)

Answer 34

Yes I'm back now @ganeshie8

Answer 35

so where are we.. :)

Answer 36

we're trying to find :-

f(g(2))

and

g(f(2))

Answer 37

for f(g(2))
you have already found g(2) = -2/5

right ?

Answer 38

Can somebody please give me the answer? I am falling behind in Math! D:

Answer 39

i can help u if u want :)

Answer 40

@ganeshie8 That's fine but I can't wait much longer, I really need the answer...

Answer 41

uve disappeared halfway in between 4 days ago, and al of a sudden u want answer and cant wait -_-

Answer 42

i almost forgot about this problem ! if u could tell me where u got stuck i can give a hand...
i dont mean to be offensice, just saying : dont expect help from me without you trying it first

Answer 43

@ganeshie8
I have tried, I can't do it.

Answer 44

still stuck on this ? :)

Answer 45

@ganeshie8 Yes and I've already tried to no avail.

Answer 46

its okay, lets work it and finish

Answer 47

if i remember correctly, we're trying to do below :-

```
to do this, we need to calculate two things :-

f(g(2))

and

g(f(2))
```

Answer 48

wat didi u get for f(g(2)) ?

Answer 49

here are teh functions for reference :-
```
f(x) = 10x+ 6

g(x) = (x-6)/10
```

Answer 50

@ganeshie8 I'm honestly not sure how I'd solve that.

Answer 51

its okay, once u see me doing it, u will understand

Answer 52

to find, f(g(2))

first find g(2)

g(x) = (x-6)/10
g(2) = ?

Answer 53

simply replace x wid 2, and simplify

Answer 54

g(x) = (x-6)/10
g(2) = (2-6)/10
= ?

Answer 55

i want u simplify it