Question

Prove or disprove the following: (a) If $f(x)$ is $O(g(x))$ then $2f(x)$ is $O(2g(x))$. (b) If $f(x)$ is $O(g(x))$ then $(f(x))^2$ is $O((g(x))^2)$. Note that in these proofs you do not need to use the definition of big-O, but can use the properties for combining mathematical functions covered in lecture.

          Prove or disprove the following:
(a) If $f(x)$ is $O(g(x))$ then $2f(x)$ is $O(2g(x))$.
(b) If $f(x)$ is $O(g(x))$ then $(f(x))^2$ is $O((g(x))^2)$.
Note that in these proofs you do not need to use the definition of big-O, but can use the
properties for combining mathematical functions covered in lecture.

Prove or disprove the following:
(a) If f(x) is O(g(x)) then 2f(x) is O(2g(x)).
(b) If f(x) is O(g(x)) then (f(x))^2 is O((g(x))^2).
Note that in these proofs you do not need to use the definition of big-O, but can use the
properties for combining mathematical functions covered in lecture.

Added by Zachary R.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Prove or disprove the following: a) If f(x) is O(g(x)), then 2f(x) is O(29). b) If f(x) is O(g(x)), then f(x) is O(g(x)). Note that in these proofs, you do not need to use the definition of big-O, but can use the properties for combining mathematical functions covered in lecture.