Question

If the function $f\left(x\right)=[3.5+b\sin x]$ (where [ . ] denotes the greatest integer function) is an even function, then complete set of values of $b$ is

• A. $(-0.5,0.5)$
• B. $[-0.5,0.5]$
• C. $(0,1)$
• D. $[-1,1]$

Answer 1

Answer: (A)

$(-0.5,0.5)$

$f\left(x\right)=[3.5+bsinx]$ for $f\left(x\right)$ to be an even function.
$3<3.5+bsinx<4,\forall xϵR$
$\Rightarrow -0.5<bsinx<0.5,\forall x\in R$
$\Rightarrow -0.5<b<0.5\Rightarrow b\in (-0.5,0.5)$
Hence, (A) is the correct answer.