GrowthFunctions_InC_QA_1 Let  f ( n ) = 7 n + 3 and g ( n ) = n {"version":"1.1","math":"\text{Let } f(n) = 7n + 3 \quad \text{and} \quad g(n) = n"} Using the formal definition of Big-O notation, which of the following correctly shows that  f ( n ) ∈ O ( g ( n ) ) ? {"version":"1.1","math":"f(n) \in O(g(n))?"} 单项选择题

f ( n ) ∉ O ( n ) ,   because of the constant 3 in the function {"version":"1.1","math":"f(n) \notin O(n),\ \text{because of the constant 3 in the function} \newline "}

Let  c = 10 ,   then for all  n ≥ 1 ,   f ( n ) = 7 n + 3 ≤ c ⋅ g ( n ) = 10 n ⇒ f ( n ) ∈ O ( n ) {"version":"1.1","math":"\text{Let } c = 10,\ \text{then for all } n \ge 1,\ f(n) = 7n + 3 \le c \cdot g(n) = 10n \Rightarrow f(n) \in O(n) \newline "}

Let  c = 5 ,   then for all  n ≥ 1 ,   f ( n ) = 7 n + 3 ≤ c ⋅ g ( n ) = 5 n ⇒ f ( n ) ∈ O ( n ) {"version":"1.1","math":"\text{Let } c = 5,\ \text{then for all } n \ge 1,\ f(n) = 7n + 3 \le c \cdot g(n) = 5n \Rightarrow f(n) \in O(n) \newline"}

Let  c = 7 ,   then for all  n ≥ 1 ,   f ( n ) = 7 n + 3 ≤ c ⋅ g ( n ) = 7 n ⇒ f ( n ) ∈ O ( n ) {"version":"1.1","math":"\text{Let } c = 7,\ \text{then for all } n \ge 1,\ f(n) = 7n + 3 \le c \cdot g(n) = 7n \Rightarrow f(n) \in O(n)"}