If f x = [ array ccc x & - x & 0 x & x & 0 0 & 0 & 1 array ] , then which of the following are correct? 1. f ( ) f ( )= f ( + ) 2. The value of the determinant of the matrix f( ) f( ) is 1 . 3. The determinant of f(x) is an even function. Select the correct answer using the code given below:

Step-by-step solution

f ( )= [ array ccc & - & 0 & & 0 0 & 0 & 1 array ] & f ( ) [ array ccc & - & 0 & & 0 0 & 0 & 1 array ] aligned & f ( ) f ( )= [ array ccc - & - - & 0 + & - + & 0 0 & 0 & 1 array ] & (using Trigonometric Identities) & f ( ) f ( )= f ( + ) . & Also, det, [ f ( ) f ( )]=1 [ ^2( + )- (- ^2( + ) ) ] & = ^2( + )+ ^2( + )=1 . aligned & det .( f (x))= ( ^2 x- (- ^2 x )= ^2 x+ ^2 x=1 . . For x=-x det .( f (-x))= ^2(-x)+ Sin ^2(-x)=1 Hence, det .( f (-x))= det .( f (x)) Hence, det.( f ( x ) ) is even function.