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Functions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsFunctions1 Mark
Question
Find the range of the following function : $f(x)=\frac{1}{1+\sqrt{x}}$
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Answer

$f(x)=\frac{1}{1+\sqrt{x}}=y$, (say)
$ \therefore \sqrt{ } \mathrm{x} y+\mathrm{y}=1$
$\therefore \sqrt{\mathrm{x}}=\frac{1-y}{y} \geq 0$
$\therefore \frac{y-1}{y} \leq 0$
$\therefore 0<\mathrm{y} \leq 1 $
$\therefore$ Range of $f=(0,1]$

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