Gujarat BoardEnglish MediumSTD 11 ScienceMATHSFunctions2 Marks
Question
Find the domain and range of the following real valued functions: $\text{f(x)}=\sqrt{\text{x}-3}$
✓
Answer
Given, $\text{f(x)}=\sqrt{\text{x}-3}$ Domain(f): Clearly, f(x) assumes real values if $\text{x}-3\geq0$ $\Rightarrow\ \text{x}\geq3$ $\Rightarrow\text{x}\in[3,\infty)$ Hence, domain $(\text{f})=[3,\infty)$ Range of f : For $\text{x}\geq3,$ we have $\text{x}-3\geq0$ $\Rightarrow\ \sqrt{\text{x}-3}\geq0$ $\Rightarrow\ \text{f(x)}\geq0$ Thus, f(x) takes all real values greater than zero. Hence, range $(\text{f})=[0,\infty)$
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