JEE MATHEMATICS MCQ: FUNCTIONS

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Understanding +4 | -1

f\;:\left[ { - 4,0} \right] \to R

is given by

f\left( x \right) = {e^x} + \sin x,

its even extension to

\left[ { - 4,4} \right],

View answer and explanation

Correct option: B

{e^{ - \left| x \right|}} - \sin \left| x \right|

Option B (

{e^{ - \left| x \right|}} - \sin \left| x \right|

) is correct because it defines the even extension of the given function over the specified interval.

More Questions from FUNCTIONS

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

f(x)=x(4-x)

f^{-1}(x)

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

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

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

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

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

f: R \rightarrow R

f(x)=x^4

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

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