Question

for each x belonging to [0,1], let f(x) = x if x is rational, and let f(x) = 1-x if x is irrational. Prove that f(f(x)) = x for all x belonging [0,1].

Answer 1

so its a piecewise function eh

Answer 2

f(x) = x, or 1-x

let x = a
f(f(a)) = ((a)), or (1-(a)), or 1-(1-a)

Answer 3

maybe defining the parts of f in their own right might make this format easier to read

Answer 4

r(x) = x; i(x) = 1-x

r(r) = x
r(i) = 1-x
i(i) = 1-(1-x) = x
i(r) = 1-x

Answer 5

if x is rational, then r(r) = x, and none of the others are defined
if x is irrational, then i(i) = x, and none of the others are defined