What is the range of the fcn cos(sin(1/x)) and how did you get it?

What is the range of the fcn cos(sin(1/x)) and how did you get it?

@Mathematics

Question

What is the range of the fcn cos(sin(1/x)) and how did you get it?

@Mathematics

jamesj · Answer

Like I suggest to you earlier, consider the function g(x) = sin(1/x).  What is the range of that function?  

That range, call it R, is the domain of the function f(x) = cos(x) that you're interested in.

jamesj · Answer

Once you know the domain of f you can calculate its range.

anonymous · Answer

How are you so sure that the domain of the inner fcn is the Dom. of the outer fcn?

jamesj · Answer

I didn't say that.  I'm saying the domain of the cos will be the range of sin(1/x)

jamesj · Answer

...and now with that restricted domain, we can calculate the range of cos(sin 1/x)