Question

guys could you help me with this inverse


http://assets.openstudy.com/updates/attachments/54178fd2e4b0e37da3691c7b-st4lk3r-1410830636775-img_1447.jpg

Answer 1

looks good to me!

Answer 2

oh really?

Answer 3

what might be missing is a \(\pm\) before the radical, but not if you have restricted the domain

Answer 4

yep, all good

Answer 5

I dont know the thing is the graphing software shows this

Answer 6

the 5th line should just be x+1 not (x+1)^2 but otherwise you've got the inverse

Answer 7

ohh i see

Answer 8

but how about how the inverse is being displayed?

Answer 9

http://www.wolframalpha.com/input/?i=inverse+sqrt%288-2x-x^2%29

Answer 10

oh nice

Answer 11

guys and how many inverses can i consider from that equation?

Answer 12

you have to restrict the range of \(y=\sqrt{8-2x-x^2}\) to make it one to one

Answer 13

also what would be the domain of the inverse function? do i solve for 9-x^2 > 0 right ?.

Answer 14

two issues here
\[f(x)=\sqrt{8-2x-x^2}\] is not a one to one function
it is increasing, then decreasing, so the inverse is not a function
that is why you get the
\[y=-1\pm\sqrt{9-x^2}\]

Answer 15

you can restrict the domain of \[f(x)=\sqrt{8-2x-x^2}\]to make it one to one, that will determine whether you get
\[f^{-1}(x)=-1+\sqrt{9-x^2}\] or
\[f^{-1}(x)=-1-\sqrt{9-x^2}\]

Answer 16

as for the domain of either, you are right, you need to solve
\[9-x^2\geq 0\]

Answer 17

or else determine the range of
\[\sqrt{8-2x-x^2}\] it is the same problem

Answer 18

oh right but I didn't get quite well how would i restrict the main function do i have to take the positive side or the negative side?

Answer 19

@satellite73 hey friend how can i find the range of the first function, what i did was finding the vertex and then looking at the graph but is it possible to do i algebraically??

Answer 20

yes, find the vertex of \(8-2x-x^2\)

Answer 21

the second coordinate of the vertex is the largest value of \[8-2x-x^2\]so the largest value is the square root of that number

Answer 22

which is 3!!

Answer 23

oh so that's it

Answer 24

@satellite73 Thank you.