The value of \( f(0) \), so that the function \( f(x) = \frac{2 - (256 - 7x)^{1/8}}{(5x + 3x)^{1/5} - 2} \), \( x \neq 0 \), is continuous everywhere, is given by
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To check for continuity, analyze the limits of both the numerator and denominator as \( x \to 0 \), and ensure they match the functionâs value at that point.