Can we eat food which was smelled by my dog?

A dog has a great sense of smell. They can detect hidden things by their smell. They are trained for detecting substances by hiding smells such as coffee or paraffin. 

We can eat food that was smelled by our pet dog. They probably detect food that has been (not very long ago) eaten, if trained to do so.

Dogs follow a scent in a particular way and will start by casting widely to pick up on any scent molecules in the air.

The dog moves quickly from side to side, taking lots of fast sniffs, then moves along the path of the strong smell, as they go. 

The scent becomes existing in a small place to area, the dog slows down to survey the air to find more detail.

They even stop moving and hold their head up to scent the air or stick their nose to the ground, then take a fewer much deeper breath, to best process the scent molecules they meet. 

Dog slowly moves towards the substance they are trained to detect they will signal a 'find' in different ways.

Some dogs are trained to howl up to draw their handler's attention. Other dogs are trained to drop quietly to the ground, to alert the handler but no one else as to their find.

Dogs have a better sense of smell than people. Some dog breeds have a better sense of smell than others. This is down to the selective development of the dog nose and the scent-processing centers in the brain.

FAQS
Can I eat something after my dog licked it?
No, it's not. Dog's mouths are pretty clean because they have bacteria in them that clean their teeth. Unless your dog has dental problems or rot, I wouldn't let my dog do it because it's kind of gross getting doggy drool on your food.

Why does my dog just smell his food?
Smell. Just as it would for us, the nice smell of food can attract or discourage a dog from eating it. Maybe your dog likes strong odors, or maybe he prefers something milder. The freshness of your dog food will also affect its odor.

Can we eat food eaten by dogs?
Dog food isn't designed for the unique nutrition needs of humans, though it is made from ingredients that are technically safe for humans to eat. So, it's not basically and most poisonous for humans and maybe safe in an emergency. However, eating dog food may increase your risk of developing a foodborne illness.