Functional dependencies proving method
Here is a possible derivation:

 1. A → CD   (given)
 2. C → BE   (given)
 3. CD → BED (by augmentation of 2 with D)
 4. A → BED  (by transitivity of 1 and 3)
 5. B → F    (given)
 6. B → BF   (by augmentation of 5 with B)
 7. BED → B  (by reflexivity)
 8. A → B    (by transitivity of 4 and 7)
 9. A → BF   (by transitivity of 8 and 6)