Question

Sa se demonstreze ca functiile f:R-->R sunt bijective:
a) f(x) = 1 - x, x ∈ Q si -x, x ∈ R \ Q
b) f(x) = 1 - x, x ∈ Q si (1 - x)/(1 + x), x ∈ R \ Q

Answer 1

a) -injectivitate:
f(a)=f(b) => a=b
1-a=1-b
-a=-b
a=b
   -surjectivitate
f(x)=y
1-x=y
x=1-y ∈ R  
=> functie bijectiva