Question

Two Martians, Splott and Fizzle, have solved the equation 2x + 4 = –3x + 14. Examine the work of Splott and Fizzle. Identify any errors in the Martians’ calculations and explain, using complete sentences, what corrections they should make.
Create your own function to teach the Martians about functions. Your function must contain at least two different operations.
Using complete sentences, prove to Splott and Fizzle that your function is a legitimate function.
Using your function, explain to the Martians how to solve for f(3). Show your work and explain each step using complete sent

Answer 1

Using complete sentences, describe to the Martians how to find the inverse of your function.
The Martians ask you to explain one last thing, Ultimate Math Ambassador. 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 2

Splott Fizzle
2x + 4 = –3x + 14 2x + 4 = –3x + 14
2x + 4 + 3x = –3x + 14 + 3x 2x + 4 – 2x = –3x + 14 – 2x
5x + 4 = 14 4 = 14 – 5x
5x + 4 + 4 = 14 + 4 4 – 14 = 14 – 5x – 14
5x = 18 –12 = –5x
5 x divided by 5 is equal to 18 divided by 5 –12 + 5 = –5x + 5
x = 18 over 5
–7 = x

Answer 3

Yish this is going to take sometime lol xD have you tried answering #1 ?

Answer 4

Honestly I don't know how to.. I am literally brain dead when it comes to math. Putting letters in it didn't help either. :/ I have to have this completed by Friday along with other assignments, or I will be dropped.

Answer 5

Flvs too xD yeah I understand >.> I procrastinate myself :/

For #1 says to create a function, so it should look something like f(x) = 2x + 4

Answer 6

exactly like that or? 0.o

Answer 7

For #2 a function is basically, whatever input you give it will have a unique y output, so in other words whatever you input you're going to be given an output.

To find f(3) plug in 3 for every x into the equation, f(x) = 2x + 4 --> f(3) = 2(3) + 4

f(3) = 6 + 4 = 10

f(3) = 10

Answer 8

function *

Answer 9

is that it? o.o

Answer 10

Oh wait, it says to create your own function!

Lol make is simple for you, try f(x) = 2x + 6 >.> it's technically different xD

The inverse function is \(\ f(x)^{-1} \)

So basically: f(x) is another fancy way of saying y

y = 2x + 6

1. exchange 'y' for 'x', so it looks like: x = 2y + 6

2. subtract 6 from both sides, x - 6 = 2y

3. divide both sides by 2 to isolate y

4. \(\ \dfrac{x-6}{2} = \dfrac{2y}{2} \)

And that's your inverse function, just put f(x) back. So, \(\ \dfrac{x-6}{2} = f(x) \)

Answer 11

what about the first part of the question?

Answer 12

It says to examine their work, the layout provided looks messy i can't tell if it's a part. Can you fix it into 2 separate comments?

Answer 13

Examine the work of Splott and Fizzle. Identify any errors in the Martians’ calculations and explain, using complete sentences, what corrections they should make. Create your own function to teach the Martians about functions. Your function must contain at least two different operations. Using complete sentences, prove to Splott and Fizzle that your function is a legitimate function. Using your function, explain to the Martians how to solve for f(3). Show your work and explain each step using complete sent

Answer 14

Using complete sentences, describe to the Martians how to find the inverse of your function. The Martians ask you to explain one last thing, Ultimate Math Ambassador. 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 15

No i mean the work they did

Answer 16

oohhh okay!!

Answer 17

Yup ;p

Answer 18

@Emine<3

Answer 19

splott
2x+4=-3+14
2x + 4 + 3x = –3x + 14 + 3x
5x + 4 = 14
5x + 4 + 4 = 14 + 4
5x = 18 –12 = –5x
5 x divided by 5 is equal to 18 divided by 5
x = 18 over 5

Answer 20

Fizzle
2x + 4 = –3x + 14
2x + 4 – 2x = –3x + 14 – 2x
4 = 14 – 5x
4 – 14 = 14 – 5x – 14

–12 + 5 = –5x + 5
–7 = x

Answer 21

is that better?

Answer 22

Yesh :>

Answer 23

okay! :)

Answer 24

Splott 2x + 4 = -3x + 14

Subtract 4 from both sides,

2x = -3x + 10

add 3x to both sides,

5x = 10
/5 /5

x = 2 <-- what she should have gotten


He failed when he added 4 to both sides, he should have subtracted it so they would cancel out. Anything below that is considered incorrect. I don't know where he got 5x = 18 - 12 = -5x >.>




Fizzle -

He failed miserably, his calculations are off, 4 - 14 = -10 not -12, because he messed up there, anything he continues to do using that wrong calculation will be incorrect. No clue how he go this either o.0 –12 + 5 = –5x + 5 ... I think he tried to add 5x to both sides. 5x is being multiplied not added, therefore the inverse of multiplication is division, he should have divided both sides by -5 if that was what he intended.

Answer 25

well then.. Im glad some of us are gifted.. lol I would have terribly BSed that.

Answer 26

xD

Answer 27

Sill need help on the last ones?

Answer 28

yes, sorry!! >.<

Answer 29

It's k xD no worries :>

I believe this is the last one "The Martians ask you to explain one last thing, Ultimate Math Ambassador. 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."

Do you know function compositions?

Answer 30

uhmm no?

Answer 31

f(x) = 2x + 6
The inverse function is f(x)−1
y y = 2x + 6 1.
x = 2y + 6 2.
x - 6 = 2y 3.
y 4. x−62=2y2
x−62=f(x)

would this work as the created function?

Answer 32

hmm, kk

Well technically no, assigning any number to 'x' will not give you the same answer because when they're 2 separate functions. Lemme double check

Answer 33

hmmm okay..

Answer 34

Yeah pretty sure lol,

always remember that it's being raised to a power :P

\(\ f(x)^{-1} \)

Answer 35

so is that how i would submit it? o.0

Answer 36

f(x) = 2x + 6 is a function yes, the inverse would be,

\(\ f(x)^{-1} \rightarrow y = 2x + 6 \rightarrow x = 2y + 6 \rightarrow x - 6 = 2y \rightarrow \dfrac{x-6}{2} = \dfrac{2y}{2}\)

So \(\ \dfrac{x-6}{2} = y \) or \( f(x) = \dfrac{x-6}{2} \)

Now you create a new function, h(x) = ?

Answer 37

uhm?

Answer 38

Create a new function now :P

Answer 39

how would i do that?

Answer 40

I just gave you your inverse function for f(x) = 2x + 6 cx

Anything you would like -- preferably easy lol

Try something like h(x) = 4x

Answer 41

um, h(x) = 2x + 8 ? agree?

Answer 42

yes!

Answer 43

kk sec

Answer 44

okay!

Answer 45

ok, so using 2x + 8

h(2) = 2(2) + 8
h(2) = 4 + 8
h(2) = 12

Now take that result and plug it in f(x), f(x) = 2x + 6

f(h(2)) = f(12) = 30

understand?

Answer 46

is that how I would submit this? o.0 or?

Answer 47

Ok just put the basic xD sole f(h(x)) and h(f(x)) and just say that they're \(\ aren't \) the same sometimes

Answer 48

solve *

Answer 49

what???

Answer 50

if im annoying or wasting your time you don't have to help. you've already done a lot! I just don't understand anything.

Answer 51

Nah it's fine :p let's just finish the last question ;D

Answer 52

...This is the last question, right o.0

Answer 53

I understand what you are trying to tell me its just that I dont understand what itll look like to submit it. you know?

Answer 54

and yes lol