jee-advanced 1998 Q23

jee-advanced · India Composite & Inverse Functions Recover a Function from a Composition or Functional Equation

23. If $g ( f ( x ) ) = | \sin x |$ and $f ( g ( x ) ) = ( \sin \sqrt { } x ) 2$, then :
(A) $f ( x ) = \sin 2 x , g ( x ) = \sqrt { } x$
(B) $f ( x ) = \sin x , g ( x ) = | x |$
(C) $f ( x ) = x 2 , g ( x ) = \sin \sqrt { } x$
(D) $f$ and $g$ cannot be determined

23. If $g ( f ( x ) ) = | \sin x |$ and $f ( g ( x ) ) = ( \sin \sqrt { } x ) 2$, then :\\
(A) $f ( x ) = \sin 2 x , g ( x ) = \sqrt { } x$\\
(B) $f ( x ) = \sin x , g ( x ) = | x |$\\
(C) $f ( x ) = x 2 , g ( x ) = \sin \sqrt { } x$\\
(D) $f$ and $g$ cannot be determined\\

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