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RELATIONS AND FUNCTIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsRELATIONS AND FUNCTIONS2 Marks
Question
Let D be the domain of the real valued function f defined by $\text{f}(\text{x})=\sqrt{25-\text{x}^2}.$ Then, write D.
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Answer

Consider the given function, $\text{f}(\text{x})=\sqrt{25-\text{x}^2}$
For f(x) to be real, the term inside the square root can’t be negative
i.e., $25-\text{x}^2\geq0$
$\Rightarrow\ \text{x}^2\leq25$
$\Rightarrow\ 5\leq\text{x}\leq-5$
Therefore, the domain of the function, f(x) is given by D = [-5, 5]

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