How can the functionality of is.finite() be incorporated into the base::mean() function?

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Incorporating the functionality of is.finite() into the base::mean() function can be done using the following steps:

1. Create a new function that wraps around the original mean() function and uses is.finite() to remove any infinite or NA values from the input vector.

2. The new function should have the same argument names and types as the original function, but with an additional argument that specifies whether to remove infinite or NA values (or both) before computing the mean.

3. Use ifelse() statements within the new function to check if there are infinite or NA values in the input vector, and remove them as per the user-specified argument.

4. Apply the mean() function to the cleaned input vector and return the result.

Here's a code example that demonstrates the above steps:

my_mean <- function(x, na.rm = FALSE, inf.rm = FALSE) {
  if (inf.rm == TRUE) {
    x <- x[is.finite(x)]
  }
  if (na.rm == TRUE) {
    x <- x[!is.na(x)]
  }
  mean(x)
}

# Example usage:
x <- c(1, 2, -Inf, 4, NA, 6)
my_mean(x)       # Output: [1] NA
my_mean(x, na.rm = TRUE)    # Output: [1] 3.25
my_mean(x, inf.rm = TRUE)   # Output: [1] 3.25
my_mean(x, na.rm = TRUE, inf.rm = TRUE)   # Output: [1] 3.5

In this example, the new my_mean() function takes an input vector x and two optional arguments - na.rm and inf.rm, which indicate whether to remove NA and/or infinite values from x before computing the mean. The ifelse() statements inside the function are used to conditionally remove infinite and/or NA values from x using the is.finite() and !is.na() functions. Finally, the mean() function is applied to the cleaned input vector and the result is returned.