The www before your domain name is a subdomain, not part of the domain name itself. Therefore, if you set up your www CNAME record to point to your primary A record, your site will resolve both at www.coolexample.com and coolexample.com.
If you can reach your website by typing in your domain without the www but cannot reach it when you type the www, then your CNAME might be set up incorrectly.
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