Question

The range of the function
$f\left(x\right)=\sin (x{e}^{\left[x\right]}+x^2-x),\forall xϵ(-1,\infty )$ where $\left[x\right]$ denotes the greatest integer function is :

• A. $\varphi$
• B. $[0,1]$
• C. $[-1,1]$
• D. $R$

Answer 1

Answer: (C)

$[-1,1]$

Since $-1\le \sin x\le 1\Rightarrow \forall \cdot xϵ(-1,\infty )$
$\Rightarrow \sin (x{e}^{\left[x\right]}+x^2-x)\Rightarrow [-1,1]$