Gujarat BoardEnglish MediumSTD 11 ScienceMATHSFunctions1 Mark
Question
Write the domain and range of function f(x) given by $\text{f(x)}=\frac{1}{\sqrt{\text{x}-|\text{x}|}}$
✓
Answer
We have, $\text{f(x)}=\frac{1}{\sqrt{\text{x}-|\text{x}|}}$ We know that, $|\text{x}|=\begin{cases}\text{x},&\text{if x}\geq0\\-\text{x},&\text{if x}<0\end{cases}$ $\Rightarrow\text{x}-|\text{x}|=|\text{x}|=\begin{cases}\text{x}-\text{x}=0,&\text{if x }\geq0\\\text{x}+\text{x}=2\text{x},&\text{if x }<0\end{cases}$ $\Rightarrow\text{x}-|\text{x}|\leq0$ for all x $\Rightarrow\frac{1}{\sqrt{\text{x}-|\text{x}|}}$ does not take real values for any $\text{x}\in\text{R}$ $\Rightarrow\text{f(x)}$ is not defined for any $\text{x}\in\text{R}$ Hence, domain $(\text{f})=\phi=\text{Range(f)}$
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