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List of top Mathematics Questions on Continuity of a function

Let \( f(x) = x^2 \), \( x \in [-1, 1] \). Then which of the following are correct?
Let \( u + v + w = 3 \), \( u, v, w \in \mathbb{R} \) and \( f(x) = ux^2 + vx + w \) be such that \( f(x + y) = f(x) + f(y) + xy \) for all \( x, y \in \mathbb{R} \). Then \( f(1) \) is equal to:
If \( f(x) = \frac{3x - 4}{2x - 3} \), then \( f(f(f(x))) \) will be: