failure function tests
1 FAILURE FUNCTION
An abstract definition is:
Let be a function of . Then, is a failure function if the values of generated by , when substituted in , generate only failures in accordance with our definition of a failure. Here is a specific value of .
(ii) Let the mother function be an exponential function, say . Then is a failure function since the values of x generated by , when substituted in the mother function, generate only failures.
(iii) Let our definition of a failure be a non-Carmichael number. Let the mother function be . Then, is its failure function .
Here too our definition of a failure is a composite number and k belongs to N.