Question

How many functions f:N—>N satisfy (f(n),n)-hcf(f(n),n) <5 ?​

Answer 1

what do you mean by this question

Answer 2

Answer:

1

Step-by-step explanation:

Let us assume the function is f(x)=x+c where c is a natural number. In that case, there will always be some cases where the LCM is much greater than the HCF and the inequality will not be satisfied.Same goes for multiplication. Let us assume the function is some f(x)=cx where c is a natural number. The LCM of f(n),n will be f(n) and HCF will be n. In cases where cn−n>5, this inequality wont hold.I used similar reasoning for exponential functions. Thus the only case where this works out is f(x)=x, in which case LCM(f(n),n)=HCF(f(n),n)=n and thus the inequality will hold. So only one function is possible.