Question

If f(n) = 3n+2 and g(n) = n, then Prove that f(n) = O (g(n))

Answer 1

Explanation : 

Topic : Big O Notation

If f(n) <= c.g(n) for n>=0,

for some c>0 and n>1

Substitute f(n) = 3n+2

               3n+2 <= c(b)

When can be 3n+2 less than equal to c(n),

For above case the value of c can be anything above 4 is better. 

Eg. if we take c=4 and substitute in above equation then,

3n+2 <= 4n

        2<= 4n -3n

      2n<= n

It means for every n>= 2 at c=4, f(n)<=c.g(n).

f(n)= O (g(n))