Question

Please help, I don't know how to do this and need to know how to: Find f(x) and g(x) so that the function can be described as y = f(g(x)).

y = Four divided by x squared. + 9

Answer 1

QUESTION: Find f(x) and g(x) so that the function can be described as y = f(g(x)).

\[y=\frac{ 4 }{ x^2 } +9\]

Answer 2

@welshfella @Zyberg

Answer 3

f(g(x) means 'function of g(x) ' where g(x) has replaced the x in the original f(x)


so for example if f(x) = 3x^2 and g(x) = x - 1 then

f(g(x)) = 3(x - 1)^2

Answer 4

so what would I do in my case?

Answer 5

- so you have to sort f work backwards here

Answer 6

and how would i do that haha

Answer 7

@welshfella

Answer 8

What are your guesses? ;) It would be easier to teach you, if we knew what you are thinking.

Answer 9

suppose f(x) was x^2 + 9 what would g(x) have to be?

Answer 10

sorry gtg right now

Answer 11

@Zyberg

Answer 12

really confused...

Answer 13

I will say, that f(x) = x^2 + 9. Try to find g(x) ;)

Answer 14

what does g(x) even stand for again?

Answer 15

A function :)

Answer 16

I know but what are the differences between f(x) and g(x). is it just that they are both different functions?

Answer 17

and how did you find that f(x) = x^ +9?? Where did the 4 go?

Answer 18

You need to notice that 4 is 2^2 ;)

Answer 19

Perhaps this would help you: http://www.purplemath.com/modules/fcncomp2.htm

Answer 20

There are worked examples, so you might understand the concept better.

Answer 21

yes but then where does the "2" go.. if 4 is 2x^2

Answer 22

@phi can you help too?

Answer 23

yes But ii need to know how i can work THIS problem out, not a different one

Answer 24

one way to do this is break your formula into two steps.
can you do that ?

Answer 25

Just read the examples in the provided link and try to understand them.
That two and one x went to another function. You need to find 2 different functions from the one that is given.

Answer 26

I don't know how to start even on this problem except maybe plug in y for what f(x) is and then something for g(x)

Answer 27

thats why i came to open study, to get personalized help on this problem. the examples on the internet weren't helping much

Answer 28

y= (4/x^2) + 9

you could break that into
something + 9

Answer 29

say
g(x)= 4/x^2

and f(x)= x+9

Answer 30

or g(x)= 2/x

f(x) = x^2 + 9

Answer 31

so i could break it into 2^2

Answer 32

g(x)= 4/x^2 -9

f(x) = x+18

Answer 33

ok! i get that part

Answer 34

these are my only choices though :
f(x) = x + 9, g(x) = Four divided by x squared.
f(x) = x, g(x) = Four divided by x. + 9
f(x) = One divided by x., g(x) = Four divided by x. + 9
f(x) = Four divided by x squared., g(x) = 9

Answer 35

for each choice, in f(x)'s definition, replace x with g(x)
then use g(x)'s definition to expand. one of the choices should match
4/x^2 + 9

Answer 36

i am confused what do you mean expand.? and what even is g(x)? Im sorry/// still a bit confused

Answer 37

Here is an example.
say g(x) = x+3
and
f(x) = x/2

and we want to figure out f( g(x) )
in f(x)'s definition (i.e. x/2)
look for any "x", and replace it with g(x)
we get
f( g(x) )= g(x) /2 (we replaced x with g(x) )

next , in that new definition, replace g(x) with it's definition i.e. with (x+3)
in other words, in
g(x)/2
we put in (x+3) instead of g(x)
we get
(x+3)/2

that is f(g(x))

Answer 38

you could do that all in "one step", but it does not hurt to go slow until you get good at it.

Answer 39

oh ok, could you please do that but with this problem? I am creating a study guide and I already started o this problem and would like an example i already am working on

Answer 40

try with the first choice.

Answer 41

so g(x)=2/x and then y= 4/x^2 +9 ?

Answer 42

I mean g(x)= 4/x^ and f(x)=x+9

Answer 43

Here is the first choice
f(x) = x + 9, g(x) = Four divided by x squared.

Answer 44

yes, g(x)= 4/x^2 and f(x)= x+9

first step to finding f( g(x)) is to replace x in f's definition with g(x)

Answer 45

ok, so I would make it: f(x)= 4/x^2 + 9

Answer 46

yes

Answer 47

ok, and then what would be my next step.. Thanks for you patience btw!

Answer 48

your next step is to notice that is the answer

Answer 49

would it be this one: f(x) = Four divided by x squared., g(x) = 9

or this one: f(x) = x + 9, g(x) = Four divided by x squared.

i think that its the last one

Answer 50

you should follow the steps.
f(x)= 4/x^2 , g(x)= 9

replace x in f's definition with g(x)
we get
f( g(x))= 4/( g(x) )^2
next, replace g(x) with its definition (which is just 9)
f( g(x))= 4/9^2 = 4/81

Answer 51

your first choice gives the formula you want:
\[ f( g(x))= \frac{4}{x^2} + 9\]

Answer 52

thanks @phi