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Question
Answer the following:
Find the domain of the following function.
f(x) = `sqrt(x - x^2) + sqrt(5 - x)`
Solution
f(x) = `sqrt(x - x^2) + sqrt(5 - x)`
x – x2 ≥ 0
∴ x2 – x ≤ 0
∴ x(x – 1) ≤ 0
∴ 0 ≤ x ≤ 1 ...(i)
5 – x ≥ 0
∴ x ≤ 5 ...(ii)
Intersection of intervals given in (i) and (ii) gives
Solution set = [0, 1]
∴ Domain = [0, 1]
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