although eval is not recommended, this works:
<!DOCTYPE html>
<html>
<body>
<h2>Convert a string written in JSON format, into a JavaScript function.</h2>
<p id="demo"></p>
<script>
function test(val){return val + " it's OK;}
var someVar = "yup";
var myObj = { "func": "test(someVar);" };
document.getElementById("demo").innerHTML = eval(myObj.func);
</script>
</body>
</html>