Question

Can some one help me? Algebra 2

Answer 1

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

Answer 2

I made 3x + 12

Answer 3

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

Answer 4

Your equation is a function as long as the exponent raised to y is one and any term is either positive or negative but not both. eg\[y =\pm \sqrt{x}\]is NOT a function because the square root is preceded by both a positive and a negative sign.

Answer 5

Thanks @calculusfunctions can you help with a couple more function?

Answer 6

questions

Answer 7

Absolutely! What do you need? While you're typing, I'll be back in a couple of minutes. Go ahead.

Answer 8

Thanks :)

Answer 9

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

Answer 10

F(3) = 3(3) + 12
9 + 12
=21

Answer 11

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

Answer 12

I got x-12/3 Is that right?

Answer 13

First the above f(3) is correct. Now to find the inverse, i). rewrite y = f(x) (instead of writing f(x), write y), ii). interchange x and y, iii). solve for y, and and iv). rewrite \[y =f ^{-1}(x)\]In other words, change the y into that symbol.

Answer 14

So instead of 3x + 12, the inverse would be x-12/3 since it's equal to y

Answer 15

The way you've shown me is incorrect. If you meant (x - 12)/3, then you would be right! \[f ^{-1}(x)=\frac{ x -12 }{ 3 }\]OR\[f ^{-1}(x)=\frac{ 1 }{ 3 }x -4\]

Answer 16

Understood?!

Answer 17

Yes, thank you :) one last question

Answer 18

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 19

Yes? Go ahead!

Answer 20

First, as a rule

Answer 21

Sorry, I hit post by error.

First as a rule \[f(h(x)) \neq h(f(x))\]

Answer 22

So you're saying the rule is that it will never equal.

Answer 23

That's correct! However you need to demonstrate that by answering the above question.

Answer 24

Oh ok, so I will say that x = 4

Answer 25

h(x) = 5x - 23

Answer 26

I just make something up, right?

Answer 27

Boring! Can you not be a tad more creative? Does it always have to be a linear function? But alright go ahead if you must.

Answer 28

Lol what about h(x) = -6x/ 2 +45

Answer 29

You do realize that you just gave me another linear function, right?

Answer 30

No, I truly suck at functions

Answer 31

LOL. It's okay, I can be patient. After all I'm a teacher. I have to be patient!

Answer 32

How about a quadratic, cubic, square root, or even a trig or a logarithm function? Anything?

Answer 33

Um, just to warn you, the more complex the function, stupid is what I become lol. But how about h(x) = 6^2 + x - 42 ?

Answer 34

Please don't tell me it's still a linear function

Answer 35

@calculusfunctions ?

Answer 36

Sorry, I'm experiencing issues with my internet. Please be patient. I'll try to fix it.

Answer 37

Sorry, I just thought you left

Answer 38

I know you're joking but never underestimate yourself or sell your self short. If I thought or for one second believed that anyone is stupid as you put it, I wouldn't be here and I wouldn't love teaching as much as I do. You're obviously motivated to learn, which automatically makes you NOT stupid!! You're here to learn and it is my job to teach. Now, you meant to say\[h(x) =6x ^{2}+x -42\]which is a quadratic function. Good finally something different. I thought you just loved linear functions or something. Okay go a head and complete the question and show me your work when you're done.

Answer 39

Be back in a moment while you're working it out.

Answer 40

X = 4

h(4) = 6(4)^2 + 4 - 42
h(4) = 6*16 + 4 - 42
= 96 + 4 -42
= 100 - 42
= 58

Answer 41

Is that how the "6x^2" suppose to have went ?

Answer 42

Yes that is correct! That's your h(4), now find f(h(4)).

Answer 43

h(4) = 58 as you said. Thus f(h(4)) = ?

Answer 44

Ok, here's were I have problems "f(h(4))" I could never truly understand this part, could you explain the steps

Answer 45

I might have to go soon, thanks for you help :)

Answer 46

f(h(x)) is what you would call a composition of two functions or better known as composite functions. Composite functions are where the output of the inside function is the input of the outside function. In other words, the outer function is evaluated at the value of the inner function. Hence here your inside function is h(x) and when x = 4, h(x) = 58. Thus f(h(4)) = f(58). Thus now f(58) = ?

Answer 47

f(58) = h(58)

Answer 48

Sorry, I'm a slow typer because I like to make sure I'm not making errors. Plus the internet problems don't exactly help either!

Answer 49

It's ok

Answer 50

No, that is not what I said. h(4) = 58 so then f(h(4)) = f(58) = 3(58) + 12 = ?

Answer 51

OH! 58 * 3
= 174 + 12
=186

Answer 52

YES! Therefore f(h(4)) = 186. Understand?

Answer 53

Yes, thank you so much :)

Answer 54

More than welcome. Anytime but you're not finished yet. Now you have to find h(f(4) and show that f(h(4) does not equal h(f(4)).

Answer 55

:( Ok f(4) = 3(4) + 12
= 12 + 12
=24

h(24) = 6(24)^2 + 4 - 42
6* 576 +4 - 42
3456 +4 -42
3460 -42
= 3418

Answer 56

Perfect! I hate to say I told you so but see I told you you're smart!

Answer 57

:)

Answer 58

Anything else?

Answer 59

Nope

Answer 60

Okay then Good Luck and good bye for now. I log in time to time when I have free time from my regular teaching job and I'm bored. You can look for me if you need anything