Let f : R+ → R, where R+ is the set of all positive real numbers, be such that f(x) = log e x.
(i) the image set of the domain of f
(ii) {x : f(x) = – 2}
(iii) whether f(xy) = f(x) + f(y) holds.

Dear Student,
Please find below the solution to the asked query:

fx=logex As log is defined for positive value only , henceDomain is x0,As we know y=logex gives x=eyand ey is positive for all value of y, hence  x=ey will be defined for all y.Hence range image of domain  is -,ifx=-2 logex=-2x=e-2iiifx= logexfy= logeyfxy= logexy=logex+logey  As logamn=logam+logan=fx+fyHence fxy=fx+fy holds

Hope this information will clear your doubts about this topic.

If you have any doubts just ask here on the ask and answer forum and our experts will try to help you out as soon as possible.

  • 1
What are you looking for?