Let f be a function defined as f(x) = 2x + log2x over the interval [1, 2]. What conclusion can be made about the value of k such that f(k) = 4?

The function f(x) = 2x + log₂(x) is continuous on [1, 2], since both terms are continuous there. Its endpoint values are f(1) = 2 and f(2) = 5. Because 4 lies between 2 and 5, the Intermediate Value Theorem guarantees some k between 1 and 2 for which f(k) = 4. Thus, the value of k must be between 1 and 2.

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