First, you declared $db outside the function. If you want to use it inside the function, you should put this at the begining of your function code:
global $db;
And I guess, when you wrote:
if($result->num_rows){
return (mysqli_result($query, 0) == 1) ? true : false;
what you really wanted was:
if ($result->num_rows==1) { return true; } else { return false; }