Let f:[-6,6] IR defined by f(x)=x^2-3 . Consider the following: 1. (fofof )(-1)= (fofof )(1) 2. (fofof )(-1)-4 (fofof )(1)= (f^ f )(0) Which of the above is correct?

Step-by-step solution

aligned & f ( x )= x ^2-3 & fof ( x )= f ( f ( x ))= f ( x ^2-3 )= (2^2-3 )^2-3 & =2^4-6 x ^2+9-3= x ^4-6 x ^2+6 & fof (0)=0-0+6=6 & f ( f ( f ( x )))= f ( x ^4-6 x ^2+6 )= ( x ^4-6 x ^2+6 )^2-3 & fofof (1)= ((-1)^4-6(-1)^2+6 )^2-3 & =(1-6+6)-3=-2 & fofof (1)= (1^4-6(1)^2+6 )^2-3 & =(1-6+6)-3=-2 aligned