not working google recaptcha in my php website - php

Question

I'm using bluehost as my web server.
I'm trying to implement reCAPTCHA into my email form for my website,
The mail is sent without passing through the recaptcha.
Below are some of the html codes.
<div class="letterbox">
<form method="post" name="enewsform" id="enewsform" action="enewsletter_ins.php">
<h3 class="tit2">Subscribe To Newsletter</h3>
<div style="margin-top:10px;">
<label class="tit2">Name
<input type="text" name="name" value="" /></label>
<label class="tit2">Email Address
<input type="text" name="email" value="" /></label></br>
<div class="g-recaptcha" data-sitekey="itmysitekey!!"></div>
<input type="button" value="subscribe" class="btn_letter" onclick="sendData(document.enewsform)" />
</div>
</form>
<script type="text/javascript">
<!--
function sendData(f){
if(f.name.value==""){
alert("Required to name.");
f.name.focus();
return false;
}
if(f.email.value==""){
alert("Required to email.");
f.email.focus();
return false;
}
if (f.email.value.search(/(\S+)#(\S+)\.(\S+)/) == -1 ) {
alert("Not Valid Email.");
f.email.focus();
return false;
}
f.submit();
}
//-->
</script>
Below are some of the php codes.
<?
include_once $_SERVER[DOCUMENT_ROOT]."/include/initiate.php";
if(trim($name)=="" or trim($email)==""){
alert("send errer!!");
}
$form_title=$name." 님의 Subscribe to eNewsletter 신청";
$user_name=$name;
$user_email=$email;
$body="
date : ".date("Y-m-d H:i:s")."
<hr>
Name : $name
<hr>
E-Mail : $email
";
$sql = "
insert into prd_form_data set
form_type = '3',
form_title = '".$form_title."',
user_name = '".$user_name."',
user_email = '".$user_email."',
user_content = '".$body."',
insdt = now()
";
mysql_query($sql) or error(mysql_error());
//메일발송
$comments = $body;
$mailTo = ADMIN_MAIL; // 받는 메일 주소;
$mailFrom = "inquiry#example.com"; //
$mailSubject = "Subscribe to eNewsletter";
$mailContent = $comments;
$mailHeader = "From: $mailFrom\r\n";
$mailHeader .= "MIME-Version: 1.0\r\n";
$mailHeader .= "Content-type: text/html; charset=utf-8\r\n";
$mailResult = mail ($mailTo, $mailSubject, $mailContent, $mailHeader,'-f'.$mailFrom);
?>
<form method="post" action="/" name="frm">
</form>
<script type="text/javascript">
<!--
alert("ok!!");
document.frm.submit();
//-->
</script>

Answer 1

function sendData(f){
if(f.name.value==""){
alert("Required to name.");
f.name.focus();
return false;
}
if(f.email.value==""){
alert("Required to email.");
f.email.focus();
return false;
}
if (f.email.value.search(/(\S+)#(\S+)\.(\S+)/) == -1 ) {
alert("Not Valid Email.");
f.email.focus();
return false;
}
if(document.forms["enewsform"]["g-recaptcha-response"].value==""){
alert("Please fill reCAPTCHA");
document.forms["enewsform"]["g-recaptcha-response"].focus();
return false;
}
f.submit();
}
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<script src="https://www.google.com/recaptcha/api.js"></script>
<div class="letterbox">
<form method="post" name="enewsform" id="enewsform" action="enewsletter_ins.php">
<h3 class="tit2">Subscribe To Newsletter</h3>
<div style="margin-top:10px;">
<label class="tit2">Name
<input type="text" name="name" value="" />
</label>
<br />
<label class="tit2">Email Address
<input type="text" name="email" value="" />
</label>
<br />
<div class="g-recaptcha" data-sitekey="6LeIxAcTAAAAAJcZVRqyHh71UMIEGNQ_MXjiZKhI"></div>
<input type="button" value="subscribe" class="btn_letter" onclick="sendData(document.enewsform)" />
</div>
</form>
</div>