Use the definition of “f(x) is O(g(x))” to show that 2x + 17 is O(3x).

Question

Use the definition of “f(x) is O(g(x))” to show that 2x + 17 is O(3x).

🧐 Not the exact question you are looking for?Go ask a question

Solution 1

The definition of "f(x) is O(g(x))" is that there exist constants C and k such that |f(x)| <= C|g(x)| for all x > k.

To show that 2x + 17 is O(3x), we need to find constants C and k that satisfy the above condition.

Let's take C = 7 and k = 17.

For all x > 17, we have:

|2x + 17| <= 7|3x|

2x + 17 <= 21x

17 <= 19x

x >= 17/19

So, for all x > 17, the inequality holds, which means 2x + 17 is O(3x).

This problem has been solved

Solution 2

The definition of "f(x) is O(g(x))" is that there exist constants c and k such that |f(x)| <= c|g(x)| for all x > k.

To show that 2x + 17 is O(3x), we need to find constants c and k that satisfy the above condition.

Let's take c = 1 and k = 17.

For all x > 17, we have:

|2x + 17| <= 1|3x|

2x + 17 <= 3x

17 <= x

So, for all x > 17, |2x + 17| <= 1|3x|. Therefore, by the definition of Big O notation, 2x + 17 is O(3x).

This problem has been solved

Similar Questions

4. Determine whether x3 is O(g(x)) for each of these functions g(x).a) g(x) = x2 b) g(x) = x3 c) g(x) = x2 + x3d) g(x) = x2 + x4 e) g(x) = 3x f ) g(x) = x3/2

2. Determine whether each of these functions is O(x2).a) f (x) = 17x + 11 b) f (x) = x2 + 1000 c) f (x) = x log xd) 42xf x  e) 2xf x  f) ) f (x) = (x3 + 2x)/(2x + 1)

1. Determine whether each of these functions is O(x).a) f (x) = 10 b) f (x) = 3x + 7 c) f (x) = x2 + x + 1 d) f (x) = 5 log x

Big O Notation

Explain big oh notation in brief. Find big oh of the following function:f(x) = 5x4 + 9x2 + 7x + 9.

1/1

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.