GATE Electronics and Communications (EC) 2020 Solved Papers

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Question : 5 of 65

Marks: +1, -0

A super additive function

{n} {f}(.)

satisfies the following property

f(x_{1}+x_{2}) ≥ f(x_{1})+f(x_{2})

Which of the following functions is a super additive function for

x > 1 ?

${e}^{ {x}}$
${e}^{- {x}}$
$1 {/} {x}$
$√{ {x}}$

Solution:

Let

{X}_{2}> {X}_{1}

Check Let

x_{2}=3

X_{1}=2

{e}^{ {x} 1}+{ }^{x 2}= {e}^{5}

e^{x 1}=e^{2}

e^{x{2}}=e^{3}

Then

{e}^{5}> {e}^{2}+ {e}^{3}

. Which is true

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