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Relations and Functions — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSRelations and Functions3 Marks
Question
Find the domain and Range of the function $\text{f(x)}=\frac{1}{\sqrt{\text{x}-5}}.$
✓

Answer

Given that: $\text{f(x)}=\frac{1}{\sqrt{\text{x}-5}}.$
Here, it is clear that f(x) is real when $\text{x} - 5 > 0 \Rightarrow\text{x} > 5$
Hence, the domain $=(5, \infty)$
Now to find the range put
$\text{f(x)}=\text{y}=\frac{1}{\sqrt{\text{x}-5}}$
$\Rightarrow\sqrt{\text{x}-5}=\frac{1}{\text{y}}$
$\Rightarrow\text{x}-5=\frac{1}{\text{y}^2}$
$\Rightarrow\text{x}=\frac{1}{\text{y}^2}+5$
For $\text{x}\in(5, \infty), \text{y}\in\text{R}^+.$
Hence, the range of $\text{f}=\text{R}^+.$

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