Question No. 30 / Question ID 974083
Marks: 4.00
Consider the following two functions:
\[
\begin{array}{l}
f(n)=\left\{\begin{array}{lr}
n^{3}, & 0 \leq n<10000 \\<br />
n^{2}, & \text { otherwise }
\end{array}\right. \\
g(n)=\left\{\begin{array}{lr}
n, & 0 \leq n<100 \\<br />
n^{2}+4 n, & \text { otherwise }
\end{array}\right.
\end{array}
\]
Some of the following statements are true.
- $\mathrm{f}(\mathrm{n})$ is $\mathrm{O}\left(\mathrm{n}^{3}\right)$
- $\mathrm{g}(\mathrm{n})$ is $\mathrm{O}\left(\mathrm{n}^{3}\right)$
- $\mathrm{O}(\mathrm{f}(\mathrm{n}))$ is same as $\mathrm{O}(\mathrm{g}(\mathrm{n}))$
- $\mathrm{g}(\mathrm{n})$ is $\mathrm{O}(\mathrm{n})$
E. $\mathrm{g}(\mathrm{n})$ is $\mathrm{O}\left(\mathrm{n}^{2}\right)$
Choose the most appropriate answer from the options given below:
1. A and C Only
2. A and D Only
3. A, B and C Only
4. C and E Only
