If `f(x)=sqrt(1-sqrt(1-x^2))` , then `f(x)` is (a) continuous on [-1, 1] and differentiable on (-1, 1) (b) continuous on [-1, 1] and differentiable on `(-1,\ 0)uuvarphi(0,\ 1)` (c) continuous and differentiable on [-1, 1] (d) none of these

Explanation

To solve the problem, we need to analyze the function \( f(x) = \sqrt{1 - \sqrt{1 - x^2}} \) for continuity and differentiability over the interval \([-1, 1]\).

### Step 1: Determine the Domain of \( f(x) \)

The function \( f(x) \) involves square roots, so we need to ensure that the expressions under the square roots are non-negative.

1. The innermost square root \( \sqrt{1 - x^2} \) requires:
\[
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