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Let's start from the simplest case: say I have a function $f(x)=x$, and let's say I want to define a new function (of $x$) to be its $n$-th power $(f(x))^n$. How should I write the code? I tried:

f[n_, x_] := f[n - 1, x]*f[n - 1, x]
f[1, x] = x

But the result is much different from what I wanted.

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marked as duplicate by Jacob Akkerboom, m_goldberg, Michael E2, rasher, Yves Klett Mar 12 at 10:25

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1 Answer 1

up vote 2 down vote accepted
f[x_] := x^2
f[x_, n_] := Nest[f[#] &, x, n]

f[2]
f[2, 3]

(* 
4
256
*)
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1  
@francis: Thanks for accept. Note you can write the Nest as Nest[f, x, n], I put in all the gory guts to make it (perhaps) more clear. –  rasher Mar 11 at 10:26
    
Just a note that in the original there is an underscore missing and would be better using SetDelayed, so f[1,x_]:=x. This does I think what the OP intended (though rasher's answer is better). –  Ymareth Mar 11 at 11:16

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