JEE MATHEMATICS MCQ: FUNCTIONS

1 Easy

1 of 1

Analyzing +4 | -1

Let

f(x) = {a^x}(a > 0)

be written as

f(x) = {f_1}(x) + {f_2}(x),

where

{f_1}(x)

is an even function and

{f_2}(x)

is an odd function. Then

{f_1}(x + y) + {f_1}(x - y)

equals

View answer and explanation

Correct option: D

2{f_1}(x) \cdot {f_1}(y)

Option D (

2{f_1}(x) \cdot {f_1}(y)

) is the correct answer because it results from correctly decomposing the exponential function into even and odd parts and simplifying the expression.

More Questions from FUNCTIONS

Practice All Chapter MCQs →

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