1.

Find the domain of the following functions.f(x) = \(\sqrt{x-x^2} + \sqrt {5-x}\)fx = √x-x2 + √5-x

Answer»

 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 of f = [0, 1]



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