Let f(t)=t+√31−t√3. Prove that f is a cyclic function?

1 Answer
Altrigeos
Jun 4, 2017

See below.

Explanation:

A function is cyclic if it satisty the conditon:

fn(x)=x

n is the order (not the nth derivative) that is the number of times the function is applied to itself before the cycle is complete.

f(t)=t+√31−t√3
f1(t)=t+√31−t√3+√31−t+√31−t√3√3
=t+√3+√3−3t1−t√3−t√3−3
=√3−t−1−t√3

f2(t)=√3−t+√31−t√3−1−t+√31−t√3√3
=√3−3t−t−√3−1+t√3−t√3−3=−4t−4=t

Thus it is proven that the function is cyclic.

QED

An example of a cycle:
f(1)=1+√31−(1)√3=−3.732

f(−3.732)=−0.268

f(−0.268)=1

Notice how it circles back to the first value.

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