Question

Answer the following:

Find the domain of the following function.

f(x) = `sqrt(x - x^2) + sqrt(5 - x)`

Answer 1

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]