Q221 / 270 · NDA 2016 (Phase 1) · Mathematics
Let $f(x)$ be the greatest integer function and $g(x)$ be the modulus function.
What is $(f \circ f)\left(-\frac{9}{5}\right)+(g \circ g)(-2)$ equal to?
- A–1
- Correct answerB0
- C1
- D2
Solution
$f(x) \rightarrow$ greatest integer function
$f(x)=[x]$
$g(x) \rightarrow$ modulus function
$g(x)=|x|$
$\begin{aligned}
& f \circ f(x)=f(f(x))=f([x]) \\
& f \circ f\left(-\frac{9}{5}\right)=f(-2) \quad \because\left[-\frac{9}{5}\right]=-2
\end{aligned}$
$=[-2]=-2$
$\operatorname{gog}(x)=g(|x|)$
$=\|x\|$
$=|x|$
$\begin{aligned} & \operatorname{gog}(-2)=|-2|=2 \\ & (f \circ f)\left(-\frac{9}{5}\right)+\operatorname{gog}(-2)=-2+2=0\end{aligned}$
Hence, the correct answer is option: 'B'.