Question

$Z \cup ( - \infty,0)$, where [x] denotes the greatest integer less than or equal to x is

• A. $( - \infty,0)$
• B. $f:R \rightarrow R$
• C. $f(x) = 3x - 5,$
• D. None of these

Answer 1

Answer: (C)

$f(x) = 3x - 5,$

Answer 2

For, $a - 1 < x < a \cdot \left[ \frac { x } { a } \right] = 0$

so $\lim _ { x \rightarrow a - } \left( \frac { | x | ^ { 3 } } { a } - \left[ \frac { x } { a } \right] ^ { 3 } \right) = \frac { a ^ { 3 } } { a } = a ^ { 2 }$.