Problem 3. Let (R, L, 1) be the Lebesgue measure space and let f:R+R be a function such that 65(x8 3x5 + 13x2 7x + 2) + f(0) = 89.26 + 24 + 27x2 + 3 for all x E Q. Without making any appeal to continuity, show that f is measurable with respect to L. (Hint: Be careful with interpreting the definition of f!)