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Question
Write the domain of the real function f defined by f(x) = `sqrt (25 -x^2)` [NCERT EXEMPLAR]
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Solution
\[\text{We have}, \]
\[f\left( x \right) = \sqrt{25 - x^2}\]
\[\text{The function is defined only when } 25 - x^2 \geq 0\]
\[ \Rightarrow x^2 - 25 \leq 0\]
\[ \Rightarrow \left( x + 5 \right)\left( x - 5 \right) \leq 0\]
\[ \Rightarrow x \in \left[ - 5, 5 \right]\]
\[\text{So, the domain of the given function is} \left[ - 5, 5 \right] .\]
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