My question is related to the space-time complexity to find the values of n and c by considering this question. AS we have seen that there are multiple solution for the above equation is possible. But I am confused which one we have to consider.In solution1: nO = 5 and c = 101 ; this states that we are considering the input after the size of 5 and c = 101 will give us the graph of c(g(n)) closer to f(n).In solution2: nO=1 and c=105 ; states that we are considering all input but our graph is more away than f(n)But Big(O) always states that we have to consider the graph whose  rate of growth g(n) which is greater than or equal to given algorithms rate of growth     f(n).So according to me the solution1 is best Although we are losing the five inputs but we are closer to our f(n)Or there will be another logic for this ?   
Analysis of Algorithms | Big-O Notation
asymptotics