15. Let R^+ be the set of all positive real numbers.
Let f:R^+→ R: f(x) = logex.
Find (i) range (f) (ii) {x : XE R* and f(x) = -2).
(iii) Find out whether f(xy) = f(x) + f(y) for all x, y eR*.
Answers
Answered by
2
✪ᴀɴsᴡᴇʀ✪
1)
Here,
or
f is a strictly increasing function. So its maxima and minima will occurs at end points of its domain
Now,
This is possible only if
Also,
Hence, Range of f(x) is .
2)
Here,
{ } = { }
3)
Now,
and
Tanking log on both side, we get
Hence Proved
Similar questions