Question

help me solve this: (class 11 maths)

Answer 1

Solution:

Given: f(x) = √(1-√(x²-4x+5)). We need to find its domain.

∵ √(x²-4x+5) should be ≤ 1 so as to make f(x) real.

So, √(x²-4x+5) ≤ 1

or (x²-4x+5) ≤ 1

or x²-4x+5-1 ≤ 0

or x²-4x+4 ≤ 0

or x²-2x-2x+4 ≤ 0

or x(x-2) -2(x-2) ≤ 0

or (x-2)(x-2) ≤ 0

or (x-2)² ≤ 0

or x-2 ≤ 0

or x ≤ 2

So, domain of f(x) is (-∞,2].

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