Question

Let f(x)=3x² +2x+2. For which of the following is f(x) big-O of g(x) with the given values of C and k ?

a. g(x)=x²,C=8,k=1
b. g(x)=x²,C=4,k=3
c. g(x)=x³,C=3,k=2
d. All of the above
e. None of the above

Answer 1

To determine if f(x) is big-O of g(x) for the given values of C and k, we compare the growth rates of f(x) and g(x). The answer is option b.

Step-by-step explanation:

The big O notation represents the upper bound on the growth rate of a function. To determine if f(x) is big-O of g(x) for the given values of C and k, we compare the growth rates of f(x) and g(x).

For option a, g(x) = x², C = 8, and k = 1. We compare f(x) = 3x² + 2x + 2 with C * g(x), which is 8 * x². If the growth rate of f(x) is not larger than the growth rate of 8 * x², then f(x) is big O of g(x).

Performing similar comparisons for options b and c, we find that f(x) is big O of g(x) for options a and b, but not for option c. Therefore, the answer is option b.