Question

Let f(x)=(9x^3-20)^2 and g(x)=9x^3-20.
Given that f(x)=(h^og)(x), find h(x)

Answer 1

f(x) = h(g(x))

(9x^3-20) ^2 = h( 9x^3-20)

how does h change that 9x^3 - 20 into the f(x)

Answer 2

it makes all of f(x) squared?

Answer 3

Sorry, but your f(x)=(h^og)(x) is incorrectly written. Please fix it.

Answer 4

How so?

Answer 5

Whats incorrect?

Answer 6

All that is given if that \
f(x)=(h^og)(x)

Answer 7

right so the h(x) is just squares the input

h(x)=x^2

Answer 8

f(x)=(h^og)(x) why that "^ " symbol here?

Answer 9

because I don't know how to put the o between h and g

Answer 10

thats all it is

Answer 11

" ^ " does not belong in there. I think you mean f(x) = (h o g)(x).

Answer 12

(h o g)(x), there is a character for it but i forget how to put it in

Answer 13

f(x) = (h o g)(x) is easily readable and is mathematically correct.

This is what you want to calculate. What does " (h o g)(x) " signify to you? What's its name, and what does it ask of you?

Answer 14

I have no clue bud I'm sorry

Answer 15

Just started it and it gives no info on it

Answer 16

I believe I used the word "composition" the last time I helped you. Remember that?

What math operations are required by (h o g) ?

Answer 17

"I begin with function h(x); I throw out "x" from both sides of h(x) and replace "x" with .... what? "

Answer 18

Can you complete that sentence? I want you to understand what an algebraic composite function is. I went back and looked at our previous conversation and see that I did mention "composition" then.

Answer 19

I'm lost sorry

Answer 20

i'm going to close so people don't get spammed

Answer 21

Sorry, Decarr. You'll need to decide for yourself whether or not you want to learn the meaning of algebraic compositions, and if you do, to make the necessary effort.\

Answer 22

I am sorry, I'm just slow at picking up on math

Answer 23

Oh okay I just looked up the definition I think I get it now

Answer 24

" (h o g) " denotes a composition. Functions h(x) and g(x) are given.

To find this composition, you focus on h(x). You throw out the "x" and replace it with g(x). In other words, g(x) becomes the input to function h(x).

If you take calculus later, you'll see this "composition of functions" again and again.

Answer 25

I get what you were trying to tell me I'm sorry I didn't understand but I do now

Answer 26

In this particular problem, f(x) = (h o g)(x). f(x) and g(x) are given, but h(x) is not. Our job is to determine what the function h(x) looks like.

Answer 27

Please go to the very top of this conversation. Look at f(x) and g(x).

What relationship do you see between them?

Answer 28

9x^3-20 the only difference is one is squared

Answer 29

EXACTLY RIGHT. So, based upon this, take a guess. How is h(x) definited?

Answer 30

h(x)=9x^3-20?

Answer 31

As you said before, the only difference betweeen f(x) and g(x) is that the latter is squared. Is that right? Is that your meaning?

Answer 32

Yeah

Answer 33

Let's try this: find the composition of h(x) = x^2 and g(x)= 9x^3-20.

Answer 34

That's written as (h o g)(x), same as before.

Answer 35

Use g(x) as the input to h(x), as before.

Answer 36

Decarr: we are close to finishing this. OpenStudy could be wrong in describing what you are doing now, but says you are "just looking around." I need your ongoing attention if we're to finish this problem.

Answer 37

Im here im thinking of how to put it together

Answer 38

would it be like
x(9x^3-20)^2?

Answer 39

because the example that I looked up shows kinda like that

Answer 40

type out g(x), please.

Answer 41

g(x)=x(9x^3-20)^2

Answer 42

But at the very top of this conversation, g(x) is definited as 9x^3 - 20.

h(x) is x^2.

I ask you to replace the "x" in h(x) with g(x) and the "x" in x^2 with (9x^3-20). By doing this you are forming the composition (h o g) (x).

Answer 43

h(x) is definited as h(x) = x^2.

throw out the x on both sides. Obtain h( ) = ( )^2. What goes inside those parentheses?

Answer 44

Again, you are forming the composition (h o g)(x).

It will be ( )^2

after you write 9x^3 - 20 inside those parentheses.

Answer 45

So simple? (9x^3-20)^2 or no x?

Answer 46

And thanks for putting up with me I know im frustrating

Answer 47

NO on the left. Right.

Now compare your result with f(x). Are your result and f(x) the same or different?

Answer 48

I meant NO "x" on the left. Correct.

Answer 49

(h o g)(x) = (9x^3 - 20)^2. that's all. Is this the same as f(x) or not?

Answer 50

Decarr: May I have your attention, please?

Answer 51

Sorry had to make baby sister a bottle for bed

Answer 52

And yes it is the same

Answer 53

Please let me know if you have to leave our conversation. Otherwise I sit here waiting for you without knowing the reason.

Answer 54

I apologize

Answer 55

All right. That goes to show that h(x) = x^2 is correct. We're done.

Answer 56

The algebraic operation we used again and again here is called " ? "

Answer 57

Composition right?

Answer 58

yes. very good. Hope you have a better idea of what "composition" means in algebra, and can correctly explain expressions such as (h o g)(x).

Answer 59

Yes thanks again happy new year

Answer 60

Same to you. Take care, see you again.