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Let f(x) be a continuous function defined for 1 le x le 3. If f(x) takes rational values for all x and f(2) = 10, then f(1,5) is equal to

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As f(x) is continuous in [1, 3], f(x) will attain all values between f(1) and f(3). As f(x) takes rational values for all x and there are innumerable irrational values between f(1) and f(3) which implies that f(x) has a constant rational values at all points between x=1 and x=3. So, f(2)=f(1.5)=10
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