Ok bit of help please guys - i think i'm just twisting myself in unnecessary knots!
The function:
Is the Domain [6,9] ?
How can i then find the image set of and its rule?
Thank you
Yes the domain is [6,9].
The range can be found by finding f(6) and f(9).
and so the range is [-3,0]
When taking the inverse the the domain becomes the range and the range becomes the domain. Therefore the domain of is [-3,0] and the range is [6,9]
Let
.
To determine the sign find g^{-1}(0) = 9 = 3+3\sqrt{4} = 9. So we want the positive root:
Domain: [-3,0]
Range : [6,9]