Question Bank - Mathematics

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What is the domain of the function \(f(x) =\sqrt{1 - (x-1)^2} \ ?\)

A.
(0, 1)
B.
[-1, 1]
C.
(0, 2)
D.
[0, 2]

Solution:

Concept:A function y = ?f(x) is define for f(x) > 0.If (x - a)(x - b) ? 0 ? x ? [a, b]Calculation:Given that, \(f(x) =\sqrt{1 - (x-1)^2} \ \)For a function to be defined,1 - (x - 1)2 ? 0? (x - 1)2 - 1 ? 0Since, (a - b)2 = a2 - 2ab + b2? x2 + 1 - 2x - 1 ? 0? x2 - 2x ? 0? x(x - 2) ? 0? x ? [0, 2]

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