I NEED DETIALS FOR QUESTION 1 AND 3 ONLY 2 NO

SOLUTION
1.
If f is not continuous at some point a belongs to R then there is sequence {xn}
satisfying xn→x₀ such that f(x) does not belongs to f(a). This implies that for
some €₀ >0, there is a subsequence{xnk}such thatI f(xnk)-f(a)I≥€₀.
Without loss of generality ,we assume that ,x- is monotonic and f(xnk)...