"Bijective Function: Is It Bijective?

[CarmineCortez]

Homework Statement

Is this function bijective ?

f: [0,1] --> [0,1]

f(x) = x if x E [0,1] intersection Q
f(x) = 1-x if x E [0,1]\Q

Homework Equations

The Attempt at a Solution

it is bijective for the rational numbers not sure about the irrationals.

 

[morphism]

Just manually check whether it's 1-1 (consider the different meanings of "f(x)=f(y)") and onto (draw a graph; is there anything in [0,1] that f misses?).

 

[Dick]

Why not? If x is irrational and in [0,1] then 1-x is irrational and in [0,1]. The function is pretty easy to invert.