Question
Find the domain of the function f, defined by f (x) = sqrt (x3 (9-x)).
Answer :
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Skip in 10
To find the domain of the function: \[ f(x) = \sqrt{x^3 (9 - x)} \] ### Step 1: Identify Domain Restrictions Since the function involves a square root, the expression inside the root must be non-negative: \[ x^3 (9 - x) \geq 0 \] ### Step 2: Find the Critical Points The expression inside the square root is: \[ x^3 (9 - x) \] Setting it equal to zero to find the critical points: \[ x^3 (9 - x) = 0 \] This gives the solutions: \[ x^3 = 0 \quad \Rightarrow \quad x = 0 \] \[ 9 - x = 0 \quad
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