ASP .NET Custom Validation client side code not Working

Hi,
I am trying to validate below input type using custom validator and client side validation. If I am using the Javascript code in the asp .net page ..its working fine. But if I am using same code in separate JavaScript file it is not working. I need help
Thank You
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Javascript code:

<script>
function FirstNameValidate(sender, args) {
//do your validation logic
if (document.getElementById("txtFirstName").value == '')
args.IsValid = false;
if (!args.IsValid)
var ctrl = $("#" + sender.controltovalidate);
if (ctrl) {
ctrl.css({ "border": "1px solid red" });
sender.innerHTML = "Please enter First Name.";
}
}
</script>
...................................
<asp:CustomValidator ID="firstNameValidator" runat="server" ErrorMessage="" Display="Dynamic"
ControlToValidate="txtFirstName" ForeColor="red" ValidationGroup="registerButton"
OnServerValidate="firstNameValidator_ServerValidate" ValidateEmptyText="True"
ClientValidationFunction="FirstNameValidate" SetFocusOnError="true">

<asp:TextBox ID="txtFirstName" class="form-control" placeholder="First name" runat="server">