Which is Lagrange's interpolation polynomial for the following data?
Which is Lagrange's interpolation polynomial for the following data?
x | 2 | 4
f(x) | 3 | 5
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Correct answer: (C) x + 1
Explanation
With two points, Lagrange's formula gives f(x) = 3(x−4)/(2−4) + 5(x−2)/(4−2) = −1.5x + 6 + 2.5x − 5 = x + 1. Check: f(2) = 3 and f(4) = 5.