<p>The number of points of discontinuity of \(f(x) = [2x^3 - 5]\) in \([1, 2)\) is equal to</p><p>(where \([\cdot]\) denotes the greatest integer function)</p>
Step-by-Step Solution
Key Concept: The greatest integer function has discontinuities at integer values; count the integers in the range of the inner function.
<p>For $x \in [1, 2)$, we have $2x^3 - 5 \in [2(1)^3 - 5, 2(2)^3 - 5) = [-3, 11)$</p><p>The greatest integer function $[y]$ has jump discontinuities at integer values of <span style='font-style:italic;'>y</span>.</p><p>The integer values in $[-3, 11)$ are: $-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10$</p><p>That is 14 integers. Each corresponds to a value $2x^3 - 5 = n$ for integer <span style='font-style:italic;'>n</span>.</p><p>However, we exclude the endpoint value; there are 13 discontinuities in the open interval.</p><p>∴ Answer is B.</p>
Correct Answer: B