Question

Suppose that the functions q and
r are defined as follows.

q(x)=x^2+5
r(x)= Square Root of X+7

Find the following:

(r o q)(2) = ?
(q o r)(2) = ?

Answer 1

so (r o q)(2) is a fancy way of writing r(q(2)) which means what do you get when you plug 2 into q and then that answer into r

Answer 2

so for the first one we plug 2 into q
2^2+5
4+5
9

Answer 3

now we plug that into r
9+7
15\[\sqrt{15} \]

Answer 4

So then how do you differentiate (r o q) and (q o r)? I guess more than anything I'm just confused on how to go about come about the answer. So do you think plug in
\[\sqrt{15}\](9(2)) to solve the first part, then reverse for the second? Or am I missing something. Appreciate the help.

Answer 5

wait so what is the original question you are asked then. Is it just function composition or is it asking you to differentiate the composition?

Answer 6

because above it looks to be that all your asked to do is find the composition of the functions

Answer 7

oh sorry you mean DIFFERENTIATE as in tell the difference sorry I thought you meant differentiate as in take the derivative

Answer 8

ok the way I like to think of it is like an onion

Answer 9

you work from the inside out or in the case above right to left

Answer 10

The question I need to answer is at the bottom, find the following, and plug in the answers where the question marks are. Is what you showed me all I need to do? It makes sense to me how you got there I just feel like I'm missing something to show two different answers

Answer 11

on the far right is 2

Answer 12

then to the left of that is q so you take 2 and plug it into q

Answer 13

then to its left is r so then you plug your answer from q into r

Answer 14

with the second part you see that r is to the left of 2 so you take 2 plug it into r and then into q since q is to the left of r

Answer 15

alright give me a sec to see if I understand that

Answer 16

r=\[\sqrt{2+7}\] which simplifies into r=3

and then

q=3^2+5= 9+5=14

q=14

So then for the (r o q)(2)

q=2^2+5=9

and \[\sqrt{9+7}\] = \[\sqrt{16}\] so r=4

Then what's the final step to find the solution? Or is it done? I feel like I'm making it harder than this needs to be haha

Answer 17

Would both just simply = 4?

Answer 18

Whoops, added an extra step on that

Answer 19

Wait no I didn't, forgot I did both haha. Sorry, my brain is melted it's been a long day

Answer 20

That's all there is you just plug it in like that and I don't know what you mean by them both simplifying to four. the second part with sqrt(16) obviously simplifies to four but q=14 would be the end of it

Answer 21

and sorry for my above mistake of 9+7=15. I face palmed at that one. You are right it is 16 and then the sqaure root of 16

Answer 22

Yep I realized that mistake, so (r o q)(2)=4, and (q o r)(2)=14? Thanks a lot for your help, that onion analogy really helped. I was making things more complicated than they needed to be