Question

Can someone lend me a hand? Algebra 2

Answer 1

The year is 2033, and intelligent life has been found on Mars! Little green Martians have found their way to Earth and have appointed you as the Ultimate Math Ambassador to their planet. You must help them understand how Earthlings use math

Answer 2

got to answer 6 questions on this and would like to have a second opinion on my answers :)

Answer 3

ok

Answer 4

gimme one sec to get the question typed up lol

Answer 5

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.

Answer 6

Splott solved it like this:

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

Answer 7

Fizzle solved it like this:

2x + 4 = –3x + 14
2x + 4 – 2x = –3x + 14 – 2x
4 = 14 – 5x
4 – 14 = 14 – 5x – 14
–12 = –5x
–12 + 5 = –5x + 5
–7 = x

Answer 8

were either of them correct?

Answer 9

didnt splott make an error when he added 3x to the wrong value?
2x + 4 + 3x = –3x + 14 + 3x, =3x should of been added to -3x not 14 right?

Answer 10

Splott solved it like this:

2x + 4 = –3x + 14
2x + 4 + 3x = –3x + 14 + 3x CORRECT
5x + 4 = 14 CORRECT
5x + 4 + 4 = 14 + 4 WRONG, he should have subtracted 4 both sides
5x = 18
5 x divided by 5 is equal to 18 divided by 5
x = 18 over 5

Answer 11

alright i see it, how about fizzle?

Answer 12

Fizzle solved it like this:

2x + 4 = –3x + 14
2x + 4 – 2x = –3x + 14 – 2x CORRECT
4 = 14 – 5x CORRECT
4 – 14 = 14 – 5x – 14 CORRECT
–12 = –5x WRONG, 4-14 = 10
–12 + 5 = –5x + 5 WEONG, he should gave divided -5 both sides
–7 = x

Answer 13

*have

Answer 14

Thanks man! i got a couple more questions relating to this :)

Answer 15

Create your own function to teach the Martians about functions. Your function must contain at least two different operations.

Answer 16

create something, il give u a hand... fine tuning it :)

Answer 17

alright ill give it a go!

Answer 18

5x + 4 = 3x * 2

Answer 19

will that do?

Answer 20

no, try something like below :-

f(x) = 2x + 2

or

f(x) = x^2-3x+2

Answer 21

ok

Answer 22

f(x) = 10x + 6

Answer 23

@ganeshie8

Answer 24

look s good

Answer 25

Using complete sentences, prove to Splott and Fizzle that your function is a legitimate function.

Answer 26

so what makes this a legit function? @ganeshie8

Answer 27

to prove its a legit function, we need to know the definition of function.
wats the definition of a function ?

Answer 28

I think functions will always end up with 1 answer or some rule like that?

Answer 29

In mathematics, a function[1] is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

Answer 30

so everytime we should get the exact same output?

Answer 31

so would that mean no matter what the x value is the output will be the same?

Answer 32

or would it mean that there will only be one answer but it may change if the x value is changed?

Answer 33

the latter one.
for every x value, there is a unique y value

Answer 34

f(x) = 10x + 6

if you put x = 0, u always get, y = 6
u never get any other value

Answer 35

so everytime you change the x value there will be a y value thats unique to it?

Answer 36

exactly ! u get the point :)

Answer 37

alright so how should i explain this in my answer?

Answer 38

just put wat we discussed in words

Answer 39

Just say for every x value there is a unique y value?

Answer 40

u can be more expressive

Answer 41

and then throw in an example?

Answer 42

In mathematics, a function[1] is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
that means. for every x value there is a unique y value. there are other relations that are not functions.... u can expa

Answer 43

the more more words u put, the better

Answer 44

hey if x = 1 then would y = 16?

Answer 45

@ganeshie8

Answer 46

yup

Answer 47

y^2 = x
is not a function, why ?

Answer 48

u may think of it later, after finishing the current assignment :)

Answer 49

alright i'll give it some thought :)

Answer 50

Using your function, explain to the Martians how to solve for f(3). Show your work and explain each step using complete sentences.

Answer 51

so..

f(x) = 10x + 6

y = 10x + 6?
/10

y = 6/10?

Answer 52

nopes

Answer 53

hmm

Answer 54

you wanto solve f(3)

simply replace x wid 3 in the original function

f(x) = 10x + 6
f(3) = 10*3 +6
= 30+6
= 36

Answer 55

alright I got it. :) and if it was f4 it would of been 46?

Answer 56

Using complete sentences, describe to the Martians how to find the inverse of your function.

Answer 57

@ganeshie8

Answer 58

I'm guessing the inverse would like switch everything around?

Answer 59

you got f(3) = 36 right ?
how did u get that ? u simply plugged 3 for x

Answer 60

yeah

Answer 61

now the inverse is like this :
il tell you that 36 is the value of funciton. you're supposed to find wats the input value

Answer 62

can u tell me for wat value of x, f(x) produces 56 ?

Answer 63

5

Answer 64

can u tell me for wat value of x, f(x) produces 106 ?

Answer 65

10

Answer 66

now tell me, step by step how did u get 10

Answer 67

well 10 * 10 = 100 then add 6 to get 106

Answer 68

you must have mentally done this :-

f(x) = 10x+6
106 = 10x + 6

106-6 = 10x

106-6
------ = x
10

Answer 69

Yep thats what i did, just couldnt figure out how to put it on paper lol

Answer 70

finding inverse is the samething
just solve for x first

Answer 71

alright so now i need to solve for 36?

Answer 72

f(x) = 10x+6

f(x) - 6 = 10x

f(x)-6
------ = x
10

Answer 73

now, switch f(x) and x

Answer 74

x-6
------ = f(x)
10

Answer 75

36 = 10x + 6
-6 -6
30 = 10x
/10 /10
3 = x or x = 3

Answer 76

this f(x) is ur inverse function

Answer 77

^ check my work above

Answer 78

alright so they don't want u to solve it more of just change it into a different equation?

Answer 79

correct, they want the equation for inverse function

Answer 80

sorry was afk

Answer 81

np

Answer 82

last question

Answer 83

he 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 84

wat are our two functions, f(x) , and its inverse g(x) ?
can u pull them for me and write them here please ? :)

Answer 85

yeah np

Answer 86

f(x) = 10x + 6

Answer 87

then x-6/10 = 36?

Answer 88

noo, wahts out inverse functin ?

Answer 89

whoops sorry lol

Answer 90

this is our inverse function
x-6
------ = f(x)
10

Answer 91

sine they're asking us to call the inverse function as g(x),
lets call it g(x)

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

Answer 92

so, our function is
f(x) = 10x+ 6


its inverse is
g(x) = (x-6)/10

Answer 93

now we replace x with the inverse in F?

Answer 94

Next, find f(g(x)) and g(f(x))

Answer 95

alright

Answer 96

u should get x for both. give it a try. .... i need to go run a quick errand, brb cya

Answer 97

alright