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## Homework Statement

Consider the following functions:

Modified Dirichlet Function

f(x) = 1/n if x=m/n of lowest forms, and f(x) = 0 if x is irrational

find an integrable function g(x) such that the composition of g and f is NOT integrable

## The Attempt at a Solution

Let g(x) = nx for all n in N (natural numbers)

then

h(x) = g(f(x)) = n(1/n) = 1 if x is rational, and h(x) = g(f(x))= n(0) = 0 if x is irrational

My g(x) is apparently incorrect. Can anyone tell me why?

I appreciate your help,

M

note: I already know the correct answer, I just need to confirm that the g(x) I came up with is incorrect.