```ruby
module UsersHelper
  def profile_image(user, size=24)
    user_image = user.authorizations && !user.authorizations.empty? ? user.authorizations.first.image : 'user.png'
    image_tag user_image, :width => size
  end
  
  def user_name(user)
    link_to user.name, user, :class => 'user_name'
  end

  def hex_to_rgba(hex)
    m = hex.match /#(..)(..)(..)/
    "rgba(#{m[1].hex}, #{m[2].hex}, #{m[3].hex}, .7)"
  end
end
```

Fix user_name helper; update profile_image helper
user
```ruby
module UsersHelper
  def profile_image(user, size = 24)
    image_tag user.image_file, :width => size
  end
  
  def user_name(user)
    link_to user.name || user.nickname, user, :class => 'user_name'
  end

  def hex_to_rgba(hex)
    m = hex.match /#(..)(..)(..)/
    "rgba(#{m[1].hex}, #{m[2].hex}, #{m[3].hex}, .7)"
  end
end
```
assistant