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Question: An issue in composing functions

Question:An issue in composing functions

mmcdara 6740 Maple
composition eval substitution inverse
February 10 2024
1

Hi,

How can I get y=x in output (4) when  g is equal to f?

> 

restart
> 

f := x -> F(x)

proc (x) options operator, arrow; F(x) end proc

 (1)
> 

((f@@(-1))@f)(x);

x

 (2)
> 

# Let us assume that y is defined this way

y := ((f@@(-1))@g)(x);

(f@@(-1))(g(x))

 (3)
> 

# When g is identical to f I would like to get y=x

'y' = eval(y, g=f);
'y' = eval(y, g = (x -> f(x)))

y = (f@@(-1))(F(x))

  

y = (f@@(-1))(F(x))

 (4)
> 

 

Download inverse_f.mw

Thanks in advance
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