If Adam and Eve were exempt from death, why did they need to eat?

From a Biblical point of view, it is a faulty premise to say that Adam and Eve were exempt from death. Most Christians believe that the soul is immortal because this is what they have been taught. However the Bible sustains that a soul can die. God says:

The soul that sinneth, it shall die. The son shall not bear the iniquity of the father, neither shall the father bear the iniquity of the son: the righteousness of the righteous shall be upon him, and the wickedness of the wicked shall be upon him.

Ezekiel 18:20

In fact, it was the devil's first lie.

And the serpent said unto the woman, Ye shall not surely die.

Genesis 3:4

On the other hand is the quotation from God.

But of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou eatest thereof thou shalt surely die.

Genesis 2:17

There are many profitable reasons why this belief came about. However the Bible sustains that a person that is dead simply sleeps until the Second Coming.

For the living know that they will die; But the dead know nothing, And they have no more reward, For the memory of them is forgotten.

Ecclesiastes 9:5

Jesus describes death as sleep.

These things said he: and after that he saith unto them, Our friend Lazarus sleepeth; but I go, that I may awake him out of sleep.

Then said his disciples, Lord, if he sleep, he shall do well.

Howbeit Jesus spake of his death: but they thought that he had spoken of taking of rest in sleep.

Then said Jesus unto them plainly, Lazarus is dead.

John 11:11-14

Paul describes death like sleep and clearly shows that people who die, wait until resurrection at the Second Coming.

But I do not want you to be ignorant, brethren, concerning those who have fallen asleep, lest you sorrow as others who have no hope. For if we believe that Jesus died and rose again, even so God will bring with Him those who sleep in Jesus.

For this we say to you by the word of the Lord, that we who are alive and remain until the coming of the Lord will by no means precede those who are asleep. For the Lord Himself will descend from heaven with a shout, with the voice of an archangel, and with the trumpet of God. And the dead in Christ will rise first. Then we who are alive and remain shall be caught up together with them in the clouds to meet the Lord in the air. And thus we shall always be with the Lord. Therefore comfort one another with these words.

1 Thessalonians 4:13-18

Biblically, Adam and Eve COULD die. So Biblically, if you believe they could not die, God would have been lying to them and the devil would be telling the truth(See Genesis 3:4 and Genesis 2:17 above). Jesus Himself tells us that the devil is the father of lies.

You are of your father the devil, and the desires of your father you want to do. He was a murderer from the beginning, and does not stand in the truth, because there is no truth in him. When he speaks a lie, he speaks from his own resources, for he is a liar and the father of it.

John 8:44

Adam and Eve COULD die like their Creator told them and this is why they were taken out of Eden.

Then the Lord God said, “Behold, the man has become like one of Us, to know good and evil. And now, lest he put out his hand and take also of the tree of life, and eat, and live forever”

Genesis 3:22

In order to live forever, Adam and Eve must eat from the tree of life, according to the Scripture above. This is what the tree of life is for.

Just because they had the ability to live forever doesn't mean that they would live forever. This is evident by what actually happened; they died because of sinning and becoming imperfect.

A question similar to yours could be asked. For instance: 'If Adam and Eve could not die, what would be the purpose of them breathing air?' (I don't mean to be sarcastic or snarky here.)

The point is that they would have had to obey God's laws (even natural laws like the law of gravity or the "law" of eating) if they were to live forever.

It's because the death spoken about in Genesis is not physical death. It's spiritual death. See this answer for a complete explanation.

The concept that no physical death existed before the fall doesn't make any sense from a biological standpoint. Although many who believe in the concept that physical death entered the world at the fall talk only about the death of animals, there's no scriptural reason to make this distinction. The death of a tree, a microbe, or even a skin cell, is still death. If the word "death" in Genesis meant physical death, then it ought to mean all forms of physical death of a living thing.

But that sense of death makes no sense, as every living thing of sufficient complexity depends on the death of other living things for survival. Eating (whether required or not) depends upon the death of the food (plants). Digestion involves the death of millions or billions of microbes in a persons gut and intestines. Plant life depends on rich soil, full of organic matter--organic matter is dead material from other plants and animals (insects, bacteria, etc).

In addition to Jay's excellent answer, eating was also considered a sign of fellowship and therefore acceptance (see eg Mark 2:16, Luke 5:30-32 and Galatians 2:12).

Ultimately such fellowship is meant to be had with God, as it was presumably for Adam and Eve in Genesis and as it will be:

Here I am! I stand at the door and knock. If anyone hears my voice and opens the door, I will come in and eat with that person, and they with me.

Revelation 3:20

Presumably there is purpose to food other than just maintaining life.

Revelation describes the New Jerusalem, which is generally equated with Heaven, the place where the saved will spend eternity. And according to Revelation 22:2, in this city, "In the middle of its street, and on either side of the river, was the tree of life, which bore twelve fruits, each tree yielding its fruit every month." So there is food in Heaven, even though everyone there is presumably living as an immortal soul.

Likewise at the Last Supper, Jesus said, Matthew 26:29, "But I say to you, I will not drink of this fruit of the vine from now on until that day when I drink it new with you in My Father’s kingdom.” As he died the next day, he must have been talking about something that would happen after his resurrection, when he presumably did not need food and drink to live. Also after his resurrection, he ate food on at least one occasion: Luke 24:40-43, "When He had said this, He showed them His hands and His feet. But while they still did not believe for joy, and marveled, He said to them, “Have you any food here?” So they gave Him a piece of a broiled fish and some honeycomb. And He took it and ate in their presence." (John 21 also describes Jesus having breakfast with the disciples after his resurrection, though I find that on reading it carefully, it doesn't explicitly say that HE ate anything.)

At a minimum, people enjoy eating food. I certainly do. If some pill was invented that would provide all our caloric and nutritional needs more cheaply and conveniently, I think it very likely that most people would still eat food frequently just for the pleasure of the taste and the feeling of fullness.

Beyond that I think we can only speculate. Just because you won't die without something doesn't mean that it doesn't give you other benefits.