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A function f on a measurable subset E of Rd is measurable if for all a...

A function f on a measurable subset E of Rd is measurable if for all a in R, the set

f-1([-∞,a)) = {x in E: f(x) < a} is measurable

Prove or disprove the following functions are measurable:

(a) f(x) = 8

(b) f(x) = x + 2

(c) f(x) = 3x

(d) f(x) = x2

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