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Functions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsFunctions3 Marks
Question
Find the domain and range of the following real valued functions:
$\text{f(x)}=\sqrt{\text{x}-1}$
✓

Answer

Given, $\text{f(x)}=\sqrt{\text{x}-1}$
Domain (f): Clearly, f(x) assumes real values if $\text{x}-1\geq0$
$\Rightarrow\ \text{x}\geq1$
$\Rightarrow\ \text{x}\in[1,\infty)$
Hence, domain $(\text{f})=[1,\infty)$
Range of f: For $\text{x}\geq1,$ we have,
$\text{x}-1\geq0$
$\Rightarrow\ \sqrt{\text{x}-1}\geq0$
$\Rightarrow\ \text{f(x)}\geq0$
Thus, f(x) takes all real values greater than zero.
Hence, range $(\text{f})=[0,\infty)$

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