Question

Let [t] denote the greatest integer less than or equal to t. Let f: [0, ∞) → R be a function defined by \( f(x)=\left[\frac{x}{2}+3\right]-[\sqrt{x}]\). Let S be the set of all points in the interval [0, 8] at which f is not continuous. Then \(\sum_{\mathrm{a} \in \mathrm{S}} \mathrm{a}\) is equal to ________.

Answer 1

Correct answer is 17

\(\left[\frac{x}{2}+3\right]\) is discontinuous at x = 2,4,6,8

\(\sqrt{\mathrm{x}}\) is discontinuous at x = 1,4

F(x) is discontinuous at x = 1,2,6,8

\(\sum \mathrm{a}=1+2+6+8=17\)