public async Task<HttpResponseData> GetCountries(
    [HttpTrigger(AuthorizationLevel.Function, "get", Route = "countries")] HttpRequestData req, FunctionContext ctx)
{
    var result = await _countriesService.GetCountries();            
    var response = req.CreateResponse(HttpStatusCode.OK);    
    await response.WriteAsJsonAsync(result);   
// ctx.GetCorrelationId() is an extension method on the FunctionContext 
    response.Headers.Add("x-correlationId", ctx.GetCorrelationId());        
    return response;
}

response.Headers.Add("x-correlationId", ctx.GetCorrelationId());
await response.WriteAsJsonAsync(result);