JEE MATHEMATICS MCQ: DIFFERENTIATION

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Analyzing +4 | -1

If for all

x,y \in R

, the function

f

is defined by

f\left( x \right) + f\left( y \right) + f\left( x \right)f\left( y \right) = 1

and

f\left( x \right) > 0

. Then,

View answer and explanation

Correct option: A

f'\left( x \right) = 0

for all

x \in R

Option A (

f'\left( x \right) = 0

for all

x \in R

) is correct because the given functional equation implies that

f(x)

is a constant function, hence its derivative is zero.

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