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Let f (x) = 2 + log2x (1 ≤ x ≤ 4) find the range of (1) y = [f (x)] ² + F (2x); (2) y = f (X & #178;) + F (2x)
F (x) = 2 + logx (1 ≤ x ≤ 4) is an increasing function, f (1) = 2, f (4) = 4, the range of F (x) is [2,4]; f (2x) = 2 + log (2x) = 1 + F (x), (1) let u = f (x) ∈ [2,4], y = [f (x)] & # 178; + F (2x) = u ^ 2 + U + 1 is an increasing function, its range is [7,21]; (2) f (x ^ 2) = 2 + log (x ^ 2) = 2 + 2logx = 2F (x) - 2, y = f (x)
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