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Question
Answer the following:
Find the domain of the following function.
f(x) = `sqrt(1 - sqrt(1 - sqrt(1 - x^2)`
Solution
f(x) = `sqrt(1 - sqrt(1 - sqrt(1 - x^2)`
f(x) is defined if 1 – x2 ≥ 0, `1 - sqrt(1 - x^2) ≥ 0` and `1 - sqrt(1 - sqrt(1 - x^2)) ≥ 0`
If 1 – x2 ≥ 0, then x2 ≤ 1 i.e., – 1 ≤ x ≤ 1
If – 1 ≤ x ≤ 1, then `1 - sqrt(1 - x^2) ≥ 0` and `1 - sqrt(1 - sqrt(1 - x^2)) ≥ 0`.
∴ Domain = [– 1, 1].
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