Relations and Functions — Maths STD 11 Science — Question
CBSE 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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