Question

The range of the function f(x) given by $f\left(x\right)=\frac{1}{\sqrt{x-\left[x\right]}}is$

• A. R-Z
• B. $[1,\infty )$
• C. $\left(1,\infty \right)$
• D. $\left(0,\infty \right]$

Answer 1

The correct option is C $\left(1,\infty \right)$

$\mathrm{We}\mathrm{have},0<x-\left(x\right]<1\mathrm{for}\mathrm{all}x\in R-Z\Rightarrow 0<\sqrt{x-\left(x\right]}<1\mathrm{for}\mathrm{all}x\in R-Z\Rightarrow 1<\frac{1}{\sqrt{x-\left(x\right]}}<\infty \mathrm{for}\mathrm{all}x\in R-Z\Rightarrow 1<f\left(x\right)<\infty \mathrm{for}\mathrm{all}x\in R-Z\therefore \mathrm{Range}\left(f\right)=\left(1,\infty \right)$