JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1

A real valued function

f(x)

satisfies the functional 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: D

-f(x)

Option D (

-f(x)

) is correct because by substituting specific values into the functional equation and using the given condition f(0)=1, we can derive that f(2a-x) = -f(x).

More Questions from FUNCTIONS

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f:(-\infty, 2] \longrightarrow(-\infty, 4]

, where

f(x)=x(4-x)

, then

f^{-1}(x)

is given by: If

g(f(x))=|\sin x|

and

f(g(x))=(\sin \sqrt{x})^2

, then Let

f:\left( {2,\;3} \right) \to \left( {0,\;1} \right)

be defined by

f\left( x \right) = x - \left[ x \right]

, then

{f^{ - 1}}\left( x \right)

equals Let

f: R \rightarrow R

be defined as

f(x)=x^4

, Choose the correct answer. Which of the following functions are odd functions Let

f(x)=(x+1)^2-1(x \geq-1)

. Then the set

S=\left\{x: f(x)=f^{-1}(x)\right\}

contains