Question

Let $f\left(x\right)=\sin x$, $g\left(x\right)=[x+1]$ and $g\left(f\right(x\left)\right)=h\left(x\right)$, where [.] is the greatest integer function. Then $h^{+}\left(\frac{\pi }{2}\right)$ is

• A. non existent
• B. $1$
• C. $-1$
• D. none of these

Answer 1

Answer: (B)

$1$

$f\left(x\right)=\sin \left(x\right)$ and $g\left(x\right)=[1+x]$

$\Rightarrow g\left(f\right(x\left)\right)=[1+\sin x]=h\left(x\right)$

$h^{+}\left(\frac{\pi }{2}\right)=[1+\sin (\pi /2\left)\right]=1$