Question

f(x) = cos(sin(1/x)). Is the range of this function still [-1,1]? If so, why?
f(x) = cos(sin(1/x)). Is the range of this function still [-1,1]? If so, why?
@Mathematics

Answer 1

range is the same, even if the x=0 sin(infinity) will not exceed interval [-1;1] and cos (x) if x belongs to the interval [-1;1] also wont exceed this interval.

Answer 2

on the other, sin(1/x) gives a value from interval [-1;1] and max value cos can achieve is cos(0)=1 and min value- cos(1), since cos(-x)=cos(x). So i think the correct answer is [cos(1);1)