Question

Algebra 2 question. Will using f(g(x)) and g(f(x)) result in the same number? If I use them both for y=2x+15.

Answer 1

I need to finish this in the next 5-10 minss

Answer 2

" Assign any number to x. Using complete sentences, explain whether f(g(x)) and g(f(x)) will result in the same number. "

Answer 3

f(g(x)) is not always equal g(f(x))
f(x) = x^2 + 2x
g(x) = x^3 - 1
so f(g(2)) = f(8-1) = f(7) = 49 + 14 = 63
and g(f(2)) = g(8) = 4096 - 1 = 4095
and is not equal ;)

Answer 4

can you help me do it for y=2x+15 I don't really get it.

Answer 5

@mhmdrz91

Answer 6

what is f(x) and what is g(x)? you just say y=2x+15!

Answer 7

?

Answer 8

ohh

Answer 9

they didnt give me

Answer 10

did u read the directions up there that i wrote? ^^

Answer 11

" Assign any number to x. Using complete sentences, explain whether f(g(x)) and g(f(x)) will result in the same number. "

Answer 12

i guess i have to make up something?

Answer 13

ugh

Answer 14

maybe ;)
where this question discussed?

Answer 15

its my homework

Answer 16

Does it give you a function somewhere for f(x) and g(x)? Or maybe a function for f(x), and ask you to find g(x)=inverse of f(x)?

Answer 17

hmmm @cupcake111 I think they're referring to the inverse of f(x), that is the inverse of 2x+15

do they result in the same thing, provided that g(x) is the inverse of f(x)

poor wording but I think it's what's meant

Answer 18

in which case, yes \(\bf f(f^{-1}(x)) = x, \qquad f^{-1}(f(x)) = x\)

Answer 19

assuming \(\bf g(x) = f^{-1}(x)\)

Answer 20

no it has nothing to do with inverse

Answer 21

this is what i got so far

Answer 22

so, what does it mean? :S

Answer 23

f(x)= 2x+15 if x=5

Answer 24

f(x)= 2(5)+15 f(x)= 25

Answer 25

f(x) --> y= 2x+15 f(g) ->> 25

Answer 26

and then i dont know

Answer 27

hmmm, where's the function g(x)? what is it equal to? I can see f(x) = 2x+5, but what about g(x)?

Answer 28

i haven't thought of anything

Answer 29

btw, its 2x+15, not 2x+5

Answer 30

You can't evaluate anything involving g(x) if g(x) isn't defined anywhere. Are you sure it isn't somewhere near the top of the problem set, something like that?

Answer 31

You posted above that the problem says:
" Assign any number to x. Using complete sentences, explain whether f(g(x)) and g(f(x)) will result in the same number. "

Where did you find the equation you are using for f(x)? It isn't in that statement.

Answer 32

based on the wording, g(x) is most likely the inverse of f(x)

Answer 33

it's just poorly worded really

Answer 34

its from one of the previous questions @DebbieG

Answer 35

That's what I think too. I wonder if somewhere in this problem set, you had to find g(x)=inverse of f(x)??

Answer 36

there are 6 questions in total, this is the last one, it is a lot of words but i will put it so u can see and understand better

Answer 37

OK, then what do the previous questions say about g(x)?? LOL

Answer 38

no i didnt

Answer 39

heehhe

Answer 40

lack of clairvoyant abilities put us in the precarious position to have to ask you, what's g(x)?

Answer 41

the charts got messed up

Answer 42

hmmm, take a screenshot :|

Answer 43

ok

Answer 44

Wow. Badly, badly worded. I would ask your teacher what g(x) is, or are you supposed to make one up.

Answer 45

she is not replying by text or email :(

Answer 46

i think you make one up

Answer 47

my mom doesn't even get it! sigh

Answer 48

i still have more hw... and only an hour and a half

Answer 49

Well, honestly, I think she wants you to make up f(x) (because really, it doesn't even SAY that f(x) is your made-up function, but I think it's implied) and then I suspect she wants g(x) to be the inverse of f(x). But again, it's really not spelled out in the problem.

Answer 50

:/

Answer 51

I would just use g(x)=f{inverse}(x). And then say something like, "Assuming that g(x)=f{inverse}(x)...." and proceed from there.

Answer 52

\( \text{5. Using complete sentences, describe to the Martians}\\
\\
\text{how to find the} \color{red}{\text{ inverse of your function}}\)

Answer 53

i've already done that

Answer 54

5. To find the inverse of the function, the first step is to replace the f(x) with y.
F(x)= 2x+15 will be y= 2x+15. Then, switch the x and y variables. You will have x=2y+15.
Next, solve for y by isolating it on one side of the equal sign. x-15= 2y+15-15
x-15= 2y
x-15 divided by 2 = y
x-15 over 2 = f-1(x)

Answer 55

then step 6 is to show that \(\bf f(f^{-1}(x)) = x, \qquad f^{-1}((x)) = x\\
g(x) = f^{-1}(x)\)

Answer 56

Looks good.

Answer 57

how exactly..?

Answer 58

just evaluate f(g(x)) and g(f(x)).

Plug your g(x) into f for x, and then plug your g(x) into g for x.

Answer 59

Simplify... and you should get x each time.

Answer 60

but i dont know my g(x)

Answer 61

Sure you do... you just explained to the martians how to cook it up! LOL....

Answer 62

cupcake111
i've already done that <----

Answer 63

i know..

Answer 64

well, so the inverse of 2x+15,IS g(x)

Answer 65

To find the inverse of the function, the first step is to replace the f(x) with y. F(x)= 2x+15 will be y= 2x+15. Then, switch the x and y variables. You will have x=2y+15. Next, solve for y by isolating it on one side of the equal sign. x-15= 2y+15-15 x-15= 2y x-15 divided by 2 = y x-15 over 2 = f-1(x)

\[g(x)=f ^{-1}(x)=\frac{ x-15 }{ 2 }\]and \[f(x)=2x+15\]

Answer 66

\(\bf f(x)= \color{red}{2x+15}\\
g(x) = \color{blue}{\cfrac{x-15}{2}}\\

f(g(x)) = \color{red}{2\left(\color{blue}{\cfrac{x-15}{2}}\right)+15}\\
g(f(x)) = \color{blue}{\cfrac{(\color{red}{2x+15})-15}{2}}\)

Answer 67

so simplify each, see if they give the same value

Answer 68

Ok thank u so much!! let me just do it..

Answer 69

both of u :))

Answer 70

You're welcome.

Answer 71

wait but the parenthesis for the f(g(x)) one, those big parenthesis, how do i get rid of those

Answer 72

just multiply. :) The 2 on the outside is just a product of 2 x the big fraction inside, so what will happen when you do that?

Answer 73

Something will conveniently cancel. :)

Answer 74

i cant do it!!! helpp and u can't cancel it outtt

Answer 75

@DebbieG