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A superadditive function f(.) satisfies the following property
f(x1 + x2) > f{x1) +f(x2)
Which of the following functions is a superadditive function for x > 1?
f(x1 + x2) > f{x1) +f(x2)
Which of the following functions is a superadditive function for x > 1?
- a)√x
- b)e-x
- c)ex
- d)1/x
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A superadditive function f(.) satisfies the following propertyf(x1 + x...
Verify with options
Option (a):
0.2 > 0.8 which is wrong.
Option (b)
√ 5 > 1.414 + 1.732
2.23 > 3.146 which is wrong.
Option c: ex1 + x2 > ex1 + ex2
e1 + 2 > e1 + e2
20.085 > 2.718 + 7.389 Satisfying.
Option (a):
0.2 > 0.8 which is wrong.
Option (b)
√ 5 > 1.414 + 1.732
2.23 > 3.146 which is wrong.
Option c: ex1 + x2 > ex1 + ex2
e1 + 2 > e1 + e2
20.085 > 2.718 + 7.389 Satisfying.
Most Upvoted Answer
A superadditive function f(.) satisfies the following propertyf(x1 + x...
A superadditive function f(x) satisfies the property that for any two inputs x1 and x2, the output of the function when applied to the sum of x1 and x2 is greater than or equal to the sum of the outputs when the function is applied to x1 and x2 separately.
Mathematically, for a function f(x), if it is superadditive, then:
f(x1 + x2) ≥ f(x1) + f(x2)
In other words, the function "adds more" when applied to the sum of two inputs compared to when applied to each input separately.
Mathematically, for a function f(x), if it is superadditive, then:
f(x1 + x2) ≥ f(x1) + f(x2)
In other words, the function "adds more" when applied to the sum of two inputs compared to when applied to each input separately.
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A superadditive function f(.) satisfies the following propertyf(x1 + x...
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A superadditive function f(.) satisfies the following propertyf(x1 + x2) > f{x1) +f(x2)Which of the following functions is a superadditive function for x > 1?a)√xb)e-xc)exd)1/xCorrect answer is option 'C'. Can you explain this answer?
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