Question

Write the domain of the real function f defined by f(x) = $\sqrt{25-x^2}$. [NCERT EXEMPLAR]

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ f\left(x\right)=\sqrt{25-x^2} \\ \mathrm{The}\mathrm{function}\mathrm{is}\mathrm{defined}\mathrm{only}\mathrm{when}25-x^2\ge 0 \\ \Rightarrow x^2-25\le 0 \\ \Rightarrow \left(x+5\right)\left(x-5\right)\le 0 \\ \Rightarrow x\in \left[-5,5\right] \\ \mathrm{So},\mathrm{the}\mathrm{domain}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{function}\mathrm{is}\left[-5,5\right]. \end{gathered}$$