Question

If f(x) = int(x), find the given functional value.

f(-14.321)

Answer 1

Task:

If $\mathrm{f}(\mathrm{x}) = \operatorname {int}(\mathrm{x})$ , find the given functional value. f(-14.321)

Solution:

The function $int(x)$ gives the integer part of $x$ .

It is related to the floor and ceiling functions: $\lfloor x\rfloor$ and $\lceil x\rceil$ by

$$\operatorname {int} (x) = \left\{ \begin{array}{l l} \lfloor x \rfloor & \text {for} x \geq 0 \\ \lceil x \rceil & \text {for} x < 0. \end{array} \right.$$

The integer part function satisfies

$$\operatorname {int} (- x) = - \operatorname {int} (x)$$

Proceeding from the above $f(-14.321) = [-14.321] = -15.000$

Answer: -15