Clamping a Manipulated Camera

Here is my dilemma:

EDIT: I forgot to explain what this is doing. The camera is able to be rotated around the player using the right analog stick.

While the horizontal rotation is acceptable as a 360 degree rotation, the vertical camera should only be limited to a certain angle in relation to the player. I understand moving objects can be clamped using 'Mathf' and eulers, but my question is whether or not I can clamp something controlled by an axis using those conventional methods? I am stumped as to where I would introduce the parameters.

  Any help is greatly appreciated.

Here is the code:

 public class FollowCam : MonoBehaviour {
     
     public float turnSpeed = 4.0f;
     public Transform player;
     
     private Vector3 offset;
     
     void Start () {
         transform.LookAt(player.position);
         offset = transform.position - player.position;
     }
     
     void LateUpdate()
     {
         offset = Quaternion.AngleAxis (Input.GetAxis("RightHorizontal") * turnSpeed, Vector3.up) * offset;
         offset = Quaternion.AngleAxis (Input.GetAxis("RightVertical") * turnSpeed, Vector3.right) * offset;
         transform.position = player.position + offset;
         transform.LookAt(player.position);
     }
 }