CAT 2020 Exam Shift 3 Solved Paper

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Question : 58 of 76

Marks: +1, -0

If

f(x+y)=f(x) f(y)

and

f(5)=4

, then

f(10)-f(-10)

is equal to

$0$
$15.9375$
$3$
$14.0625$

Solution:

Given

f(x+y)=f(x) f(y)

⇒ f(x)=a^{x}(

where

a

is a constant

)

Given,

f(5)=4 ⇒ a^{5}=4 ⇒ a=2^{2 / 5}

f(10)-f(-10)=a^{10}-a^{-10}=(2^{\;{2}/{5}})^{10}-(2^{\;{2}/{5}})^{-10}

=2^{4}-2^{-4}=16-\;{1}/{16}=15.9375

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