Which of these statements is not true? Select one: O a. If f(x) is (g(x)), then g(x) is 12(f(x)) ♡ O b. If f(x) is 2(g(x)), then g(x) is O(f(x)) O c. If f(x) is (g(x)), then g(x) is O(f(x)) O d. If f(x) is (g(x)), then g(x) is (f(x))

Which of these statements is not true? Select one: O a. If f(x) is (g(x)), then g(x) is 12(f(x)) ♡ O b. If f(x) is 2(g(x)), then g(x) is O(f(x)) O c. If f(x) is (g(x)), then g(x) is O(f(x)) O d. If f(x) is (g(x)), then g(x) is (f(x))
## Answer

Solution:
The answer will be an option,
(a) If f(x) is
(g(x)) then g(x) is
(f(x))
Explanation:
=>Option (a) is not true because using definition of
big-omega if f(x) =
(g(x)) then we can write f(x)
C*g(x) where C is some constant, x
x0, x0
1 so we can not write g(x)
D*g(x) where D is some constant, x
x0, x0
1.
=>Option (b) is true because using definition of big-omega if
f(x) =
(g(x)) then we can write f(x)
C*g(x) where C is some constant, x
x0, x0
1 so we can write g(x) = O(f(x)) using definition of big-O as f(x)
D*g(x) where D is some constant, x
x0, x0
1 and both relations are asymptotically equivalent.
=>Option (c) is true because using definition of big-theta we
can write C*g(x)
f(x)
D*g(x) where C and D are constants, x
x0, x0
1 hence we can write g(x) = O(f(x)) as it satisfies the definition
of big-O as f(x)
E*g(x) where E is some constant, x
x0, x0
1.
=>Option (d) is true because using definition of big-theta we
can write C*g(x)
f(x)
D*g(x) where C and D are constants, x
x0, x0
1 hence we can write g(x) =
(f(x)) as definition of big-theta E*g(x)
f(x)
F*g(x) where E and F are constants, x
x0, x0
1 hence both relations are equivalent.
I have explained each and every part with the help of statements
attached to the answer above.

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