Making Image Follow Player's z-axis

I have an image that’s acting as a background with this script attached to it.

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

public class BG_Mover : MonoBehaviour {

Transform player;

private Vector3 offset;

void Start() {
	player = GameObject.Find("Done_Player").transform;
	offset = transform.position - player.transform.position;
}

void LateUpdate() {
	transform.position = new Vector3(player.position.x, transform.position.y, transform.position.z) + offset;
}
}

What this script is supposed to do is make the image follow the player’s z coordinate, but not the x and y coordinate. Although, I made a Vector3 that is the offset of the player’s z and the image’s z. Basically, I want the difference between the player’s z and the image’s z (80) to stay the same.

Although, when I run it, the image just keeps on adding up and it flies out of the view of the camera.

What is causing the problem, and how can I fix this?

Try:

transform.position = new Vector3(transform.position.x, transform.position.y, player.position.z+80);