If [x] represent greatest integer x and [ , ] is the set of all real values of x for which the real function f(x)= 3+x + 3-x [x]+2 is defined, then f^2( +1)+5 f^2( )=

Step-by-step solution

The given function f(x)= 3+x + 3-x [x]+2 , then function f is defined if 3+x 0,3-x 0 and [x]+2>0 aligned & x -3, x 3 and [x]>-2 & x -3, x 3 and x [-1, ) & x [-1,3]=[ , ] (given) & So, =-1 and =3 aligned f^2( +1)+5 f^2( )=f^2(0)+5 f^2(3) aligned & = ( 3 + 3 2 )^2+5 ( 6 + 0 5 )^2= ( 4 3 2 )+5 ( 6 5 ) & =6+6=12 aligned Hence, option (c) is correct.