Question

Check whether the function f given by




f(x)=1/(2x-4)^2 ∀x∈]-2,2[


Is continuous in the interaval ]-2,2[.is it bounded?justify your answer.

Answer 1

Denominator of f(x) becomes 0 at x=2. Thus, it is discontinuous for x=2 only. As this point is not included in the given interval, the function is continuous in the given interval.

Further the function is bounded below, with 1/16 being the lower limit, no upper limit can be found for the given interval.