Negative predictions with R's neuralnet using ReLU act fct

Question

I am building a ANN to predict total healthcare costs (therefore a continuous variable) using a range of input variables such as age, gender, insurance coverage and number of chronic conditions. I have taken the following steps using R's neuralnet package:

1. I first standardised the values so all independent and the dependent variable values lie between 0 - 1 (using min-max rule)

2. I create a model matrix with the independent and dependent variables and also created a formula for the neural net

   df_matrix <- model.matrix(~ total_cost_stand + sex + agestand + race + inscoverage + edu_year_stand + num_cc_stand,data = df)[,-1]
   
   f <- as.formula(paste(c(colnames(df_matrix))[1], 
            paste(c(colnames(df1_matrix[,c(2:ncol(df_matrix))])), collapse = "+"), 
            sep=" ~ "))
   

3. I created training and testing dataframes

   smp_siz <- floor(0.75*nrow(df_matrix))
   
   set.seed(465) 
   
   train_ind <- sample(seq_len(nrow(df_matrix)),size = smp_siz)
   
   train_df <- as.data.frame(df_matrix[train_ind, ])
   
   test_df <- as.data.frame(df_matrix[-train_ind, ])
   

4. Given I wanted to use ReLU as the activation function I created the following function to put into neural net

   relu_copy <- function(x) ifelse(x>=0, x, 0)
   

5. Now I run the neuralnet

   nn <- neuralnet::neuralnet(f ,
                       data = train_df ,
                       hidden = c(2,2) ,
                       act.fct = relu_copy,
                       threshold = 0.01 ,
                       err.fct = "sse",
                       algorithm = "rprop+" ,
                       linear.output = TRUE)
   

However, a few of my predicted outputs are negative, which shouldn't be possible given a) all my data was standardised between 0 and 1 and b) I used a ReLU activation function, which should transform all negative values to 0.

  output <- neuralnet::compute(nn, test_df[,-1]) 

  predict <- output$net.result * (max(df$total_cost) - min(df$total_cost)) + min(df$total_cost) 
  
  min(predict)
  [1] -1447.274

I would be very grateful for any tips/explanations as to why I am getting negative prediction results.

Thanks!