Functions

[tania]

Find the domain of f(x)= sin^-1(log3(x/3))

[onionknight]

The range of the function sin(x) is [-1,1] . Therefore, the domain of the function sin^-1(y) is -[-1,1]. In the function f(x)= sin^-1(log3(x/3)), you can read log3(x/3) as y. Hence -1<log3(x/3)<1 which implies that 3^(-1) < x/3 < 3^(1) which gives us 1/3 < x <3 and finally 1<x<9 (Both included in the domain) .

Hope this helps.

[tania]

Thanks ! got it.

[Nikkita]

I think there are 2 parts:
1. Considering Sin^-1 (x) belongs to [-1,1], we get x belong to [1,9]
2. Considering log x >0 always, so x/3>0, i.e. x>3

From the intersection of above two conditions, we get x belong to (3,9].

Is it right?? Why or why not??

[Abhitesh]

(x/3) >0 i.e. x>0
The range of log x is (-inf,inf)
[1,9] is the correct answer.

[Nikkita]

Thank-you..
My silly mistake was there..