Question

Given: F(x)=xsq-7 and given f(x)=|x|, g(x)=x-7, and h(x)=x sq it is asked to write each of the following functions as in F(x)= x sq-7 as a composition of the functions chosen from f,g,h, I guess this is kind of working backwards but I don't have a clue to start. Please show me your work. Thank you.

Answer 1

By the sq do you mean square root? Something else?

Also, from what you've posted, it doesn't seem entirely clear what you need to do. I assume you need to find the function composition using f,g, and h to get F?

Answer 2

This is my first time out with this type of site. How do I acess a reply?

Answer 3

oh my actually sq should be as in x squared

Answer 4

Aylin am I still with you? Is there an answer and if so how do I find it? thank you

Answer 5

Ok, so you have\[f(x)=|x|\]\[g(x)=x-7\]\[h(x)=x^{2}\]and you need to get\[F(x)=x^{2}-7\]out of it.

Function composition is of the following form:\[(a^{o}b)(x)=a(b(x))\]

Essentially, what you are doing with the function a is putting in b(x) wherever x is. So if a(x)=7x+4, and b(x)=x-2, then a(b(x))=7(b(x))+4=7(x-2)+4=7x-10.

So what you need first is a function that turns x into x^2. Then you need a function that turns x into x-7.

Does this make sense?

Answer 6

Not yet Aylin can you give me a bit more?

Answer 7

Hmm, perhaps it would help if you went through a couple of the function compositions...

Can you find f(g(x)) and h(g(x)) for example?

Answer 8

not sure I can. I mean f would be the answer if g(x) would be the value then that value would be applied to f(x)

Answer 9

\[f(g(x))=|g(x)|=|x-7|\]\[h(g(x))=(g(x))^{2}=(x-7)^{2}=x^{2}-14x+49\]Does this make more sense now?

Answer 10

so if I start with x sq -14x +49 am I suposed to be able to derive this back to h(g(x)) Given the f(x)=|x| and the other values of g and h?

Answer 11

If you factor\[x^{2}-14x+49\]you get\[(x-7)\times (x-7)=(x-7)^{2}\]Then you know that you need a function that given an input will give an output of 7 less than the input, and another function that squares the input.

So if you have g(x)=x-7 and h(x)=x^2, you can see that h(g(x))=(g(x))^2=x^2-14x+49, so that leads you back to h(g(x)).

Answer 12

This makes sense to factor . I need to try this on some other problems and see what comes up also I just found the ^ sign for square. This is new to me ie online help so I must thank you soooo much. I will more than likely be back but I don't want to tie you up for now Berthacow

Answer 13

I'm doing other things while I help you. (Actually I'm just watching TV).

Answer 14

I am doing this on my own no school an it takes my full concentration wish it were more clear so thank you again.

Answer 15

You're welcome. It's no problem at helping.

Does the process make sense now though? If it helps you can ignore f(x) entirely for the problem you posted.

Answer 16

(This is because h(f(x))=|x|^2=x^2, which is just h(x).)

Answer 17

Alternatively, f(h(x))=|x^2|=x^2 since x^2 is necessarily positive for real numbers.

Answer 18

What I figure to do is to print this all up and so to speak use it as a template to see if it works on the other problems and see what happens.

Answer 19

ok

Answer 20

Ok you've been very kind go back to your TV and Thank you Berthacow out