Problem

Find the domain of the function \( f(x) = \frac{1}{\sqrt{5-x}} \)

Answer

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Answer

Step 3: Therefore, the domain of the function \(f(x)\) is all real numbers less than 5

Steps

Step 1 ：Step 1: Set the denominator \(5 - x\) greater than 0 for the function to be defined, i.e., \(5 - x > 0\)

Step 2 ：Step 2: Solve the inequality for x, which gives \(x < 5\) after rearranging the terms

Step 3 ：Step 3: Therefore, the domain of the function \(f(x)\) is all real numbers less than 5

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