How to compose a function n-times and want value for a particular value of n?

Suppose f(x)=x^2+1. Composition of two f, I mean f(f(x)), Similarly composition of 3 f is f(f(f(x))). n-th composition of f is denoted by f^n(x).

What is the general command to evaluate f^10(2) ?

Answer 1

[Bruno Luong]

f = @(x) x.^2-x;
n = 10;
x = 1/pi;
y = x;
for k=1:n
    y = f(y)
end
% y is f^10(x)

Answer 2

[Ameer Hamza]

Use recursion

f = @(x) x.^2 + 1;
n = 2;
fn = nRecursion(f, n);

function f = nRecursion(f, n)
    if n == 1
        f = @(x) f(f(x));
        return
    else
        f = nRecursion(f, n-1);
    end
end

f, and fn are function handles.

Example

>> f(f(5))
ans =
   677
>> fn(5)
ans =
   677
>> f(f(10))
ans =
       10202
>> fn(10)
ans =
       10202

[Sayantan Panja]

It shows :Undefined function or variable 'nRecursion'."

[Ameer Hamza]

No, Run it inside a script. It will not work directly on the command line.

You can also do it like this. Create a file named nRecursion.m in MATLAB path and paste the following code in it

function f = nRecursion(f, n)
    if n == 1
        f = @(x) f(f(x));
        return
    else
        f = nRecursion(f, n-1);
    end
end

and then run

f = @(x) x.^2 + 1;
n = 2;
fn = nRecursion(f, n);

in command window.