php - Syntax error on return statement

You have a few problems here. First of all there is no mysqli_result(), it does not exist. Instead you can fetch the row like below. Also your $connect is out of scope. You need to pass it as an argument, and as the comments point out even if mysqli_result() did exist, it still wouldn't work because of the syntax error.

function user_exists($username, $connect)
{
    $output = false;
    $username = sanitize($username);
    $query = mysqli_query($connect, "SELECT COUNT(`user_id`) FROM `users` WHERE `username` = '$username'");
    if($query) // check the query was successful before trying to fetch
    {
        $row = mysqli_fetch_row($query);
        $output = $row[0] > 0;
    }
    return $output;
}

I assume your sanitize() is doing mysqli_real_escape_string(). For best security, switch to a Prepared Statement.