Upper and lower bound of a function

Question

here is the question : find upper and lower bound of the function $$f(x)=cos(\frac{1}{x})$$ Domain of function is all Real numbers except {1} . I tried to solve it by finding the limits of $f(x)$ as $x$ approaches both from negative and positive. But, $$lim_{x\rightarrow 0} cos(\frac{1}{x})$$ (from negative or positive) is undefined as far as I know. Show me any hint please. Thank You!