Find Domain of \(f(x)=\sqrt{25-x^2}\)

📝 Question

Find the domain of the function:

\[ f(x)=\sqrt{25-x^2} \]

✅ Solution

🔹 Step 1: Condition for square root

For the function to be defined:

\[ 25-x^2 \ge 0 \] —

🔹 Step 2: Solve inequality

\[ x^2 \le 25 \]

\[ -5 \le x \le 5 \] —

🎯 Final Answer

\[ \boxed{[-5,\,5]} \]

🚀 Exam Shortcut

• Inside square root ≥ 0
• Solve quadratic inequality
• Result is closed interval