申論題

Concisely explain your answer with important computation or reasoning steps.
1. Consider the function f(x) = [x] - [x], where [x] denotes the smallest integer that is greater than or equal to x, and [x] denotes the greatest integer that is smaller than or equal to x. (That is, [x] = n ∈ Z such that n ≥ x ＞ n-1, and [x] = m ∈ Z such that m ≤ x＜m+1.)

1.6 True or False: Given any a,b ∈ such that a ＜ b, if there exists a function g(x) such that ,then f(x) = g(x)for all x ∈ [a, b].