Number 6 of attached hw assignment

Let f:R->R be a function. Let a>0. We say that f is periodic with period a if f(x+a)=f(x) for all x in R. Suppose f:R->R is periodic with period a and define g(x)=f(1/x) for x>0. Show that for all x>0 we have f([x,x+a])=g([1/(x+a),1/x]) and suppose f is not constant, then show that g is not uniformly continuous at (0,infinity)

Let f:R->R be a function. Let a>0. We say that f is periodic with period a if f(x+a)=f(x) for all x in R. Suppose f:R->R is periodic with period a and define g(x)=f(1/x) for x>0. Show that for all x>0 we have f([x,x+a])=g([1/(x+a),1/x]) and suppose f is not constant, then show that g is not uniformly continuous at (0,infinity)