Find the domain and range of the following real valued functions:… - Vidyadip

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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