the base has to be positive and different than 1.
the result has to be positive
l(x)=log base 5 of (sqrt(x+5))
AND
m(x)=log(|x|)
AND
n(x)=log((x+1)/(x-1))
I'd like to find the domain and range WITHOUT needing a graphic calculator. Any help would be appreciated!
Thanks!
Hello s3aFirst, note that if is real .
So the domain is
And since can take any positive value, its log (to any base) can take all values, positive, negative or zero. So the range is the whole of .
for all . But doesn't exist for , so the domain is
The range again is the whole of
Remember that the input to a log must be >0. Can you see what the domain is?
And, provided can take all positive values, can take all real values.
Grandad
If and then the domain of the function is and the range of the function is
to l:
Calculating the domain:
Since
to m:
According to my previous considerations you'll get: and
to n:
Calculating d:
and therefore:
If then and therefore ;
If then and therefore ;
Since the graph of n approaches the x-axis.
Therefore