Question

If $f$ be the greatest integer function defined as $f\left(x\right)=\left[x\right]$ and $g$ be the modulus function defined as $g\left(x\right)=\left|x\right|$, then the value of gof $\left(-\frac{5}{4}\right)$ is

• A. $\frac{1}{2}$
• B. $0$
• C. $2$
• D. does not exist

Answer 1

The correct option is C

$2$

Find the value of gof $\left(-\frac{5}{4}\right)$:

Given, $f\left(x\right)=\left[x\right]$ and $g\left(x\right)=\left|x\right|$

As we know,

$\begin{array}{rcl}\left(-\frac{5}{4}\right)& =& g\left(f\left(-\frac{5}{4}\right)\right)\end{array}$

now,

$\begin{array}{rcl}f\left(-\frac{5}{4}\right)& =& \left[\frac{-5}{4}\right]\\ & =& \left[-1.25\right]\\ & =& -2\end{array}$

$\therefore$gof $\begin{array}{rcl}\left(-\frac{5}{4}\right)& =& g\left(f\left(-\frac{5}{4}\right)\right)\end{array}$

$\begin{array}{rcl}& =& g(-2)\\ & =& |-2|\\ & =& \mathbf{2}\end{array}$

Hence, Option ‘C’ is Correct.