Why is R dplyr::mutate inconsistent with custom functions

sin and ^ are vectorized, so they natively operate on each individual value, rather than on the whole vector of values. f is not vectorized. But you can do f = Vectorize(f) and it will operate on each individual value as well.

y1 <- mutate(df, asq=a^2, fout=f(a), gout=g(a))
y1

    a   asq     fout       gout
1   0     0 3640.889  0.0000000
2  10   100 3640.889 -0.5440211
3 100 10000 3640.889 -0.5063656

f = Vectorize(f)

y1a <- mutate(df, asq=a^2, fout=f(a), gout=g(a))
y1a

    a   asq        fout       gout
1   0     0    10.88874  0.0000000
2  10   100  1010.88874 -0.5440211
3 100 10000 10010.88874 -0.5063656

Some additional info on vectorization here, here, and here.

We can loop through each element of 'a' using map and apply the function f

library(tidyverse)
df %>%
    mutate(asq = a^2, fout = map_dbl(a, f), gout = g(a)) 
#    a   asq        fout       gout
#1   0     0    10.88874  0.0000000
#2  10   100  1010.88874 -0.5440211
#3 100 10000 10010.88874 -0.5063656