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Expert: - 12/25/2008


Question
Let   ƒ(x)=√(1-x^2 )∈R.the maximum domain for which  ƒ is defined is [-1,1],
Since 1-x^2≥0
⟹ x^2≤1
⟹|x|≤1
⟹-1≤x≤1
I could not understand the example.please describe the avobe example


Answer
Here, since f(x) is defined under real domain (∈R), so the chunk under the square root sign must be positive, otherwise it extends to complex domain.

So 1-x^2≥0
    x^2≤1
    |x|≤1
    -1≤x≤1
Besides, since x^2 is always positive, the chunk under the square root is always less than 1, so 0≤f(x)≤1
Somehow the standard square root is not used here, so negative numbers are accepted, so f(x) can be negative, -1≤f(x)≤1, very weird though.

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