JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1

A real valued function

f(x)

satisfies the function equation

f(x-y)=f(x) f(y)-f(a-x) f(a+y)

where

a

is a given constant and

f(0)=1, f(2 a-x)

is equal to

View answer and explanation

Correct option: C

-f(x)

Option C (

-f(x)

) is correct because substituting

f(0)=1

and

f(a)=0

into the given functional equation leads to

f(2a-x) = -f(x)

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