# `↢` — After

Keys: `Alt-,`

`f↢g Y` is `Y f(g Y)`. The left argument of `f` is `Y` itself. For
`f(g Y)`, use [Atop](atop.qmd), `f∘g`.

``` bpl
×↢- 5              ⍝ ¯25
```

`X f↢g Y` is `X f(g Y)`.

``` bpl
10 +↢- 3           ⍝ 7
"abc" ,↢⌽ "de"     ⍝ "abced"
```

`f↢A` binds the right argument. The bound function takes one argument. A
literal argument after a space joins a literal operand’s strand:
`-↢10 3` binds the vector `10 3` and has no argument. Use `-↢10⊢3`,
`-↢10(3)`, or a named argument.

``` bpl
-↢10⊢3            ⍝ ¯7
y←3 ⋄ -↢10 y       ⍝ ¯7
```

See [Before](before.qmd), [Atop / Rank](rank.qmd) and [Over](over.qmd).

## Inverse

With an array operand, `(f↢X)⁻¹Y` inverts `f` with `X` fixed on the
right. With two functions, `X(f↢g)⁻¹Y` inverts `f` with `X` fixed, then
applies `g⁻¹`. The hook `(×↢*)⁻¹` gives the Lambert W function.

``` bpl
(-↢3)⁻¹7   ⍝ 10
(×↢*)⁻¹1   ⍝ 0.567143290409784
```