1tht log of something lies between -1 to 1 and then we square it because its square root.......so thn it becomes lies between 1 to 1
1) Find the domain of
f(x) = cos^{-1}\sqrt{log_{[x]}(\left|x \right|/x)}
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7 Answers
112) Find the domain of definition of the single valued branches of the function (What does this question mean, esp domain of definition ??)
10x + 10y = 10
62for the 1st one the square root should lie in the interval of -1 to 1
whihc means log of whatever it be lies in the interval of 0 to 1
which means that first [x]>0
moreover, |x|=x if x>0
so we can say that if [x]>0 and [x] not equal to 1 (because the base cannot be 1)
then the function will be defined..
so we want [x]>1
so x>=2 is the required inteval.....
62in the 2nd one, the domain stands for the values of x for whihc y will have real values..
the answer to that one is not too difficult either..
jut give it a good attempt..
110x+10Y=10
10Y=10-10X
TAKING log10 BOTH SIDE
Y=log(10-10x)
10-10x> or x<1
so domain is x (-infinite,1)
thats x and y gonna be to the power.......
THANKS...............
11@ SHUBH THEN IT LIES IN BETWEEN 0 AND 1............