Attached is a function qns......now studying for a test and come across problems which i have difficulty completing.... thanks for ur help in advance!
A function is defined by:
where and are positive constants.
(a) i. Find (where ).
(ii) Given that , find the values of and .
From part (i) we know that the coefficient of is , so we have . or .
We also know that the constant term is , which when we substitute in the known value of gives us .
(other parts to follow in another post if someone else does not provide their solutions first).
Another function is defined by .
(b) (i) Find in terms of and the range of .
With the definition of the range of is the open interval , which will map to the open interval
(ii) If , determine, with a reason, whether exists.
With the give devinition of we have , and the range of is the open interval . But is defined everywhere on this interval and single valued, so if:
then , and is the only such with image under of