Find the domain and range of the real function f defined by f(x) … - Vidyadip

Question

Find the domain and range of the real function f defined by $f(x) = \sqrt {x - 1} $

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Answer

Here f (x) = $\sqrt {x - 1} $, f (x) assumes real values if $x - 1 \geqslant 0 \Rightarrow x \geqslant 1$
$ \Rightarrow x \in \left[ {1,\infty } \right)$
$\therefore$ Domain of f(x) $ = \left[ {1,\infty } \right)$
For $x \geqslant 1,f(x) \geqslant 0$
Range of f (x) = all real numbers $ \geqslant 0$
$ = \left[ {0,\infty } \right)$

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