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Let f:[-6,6]toR be defined by f(x)=x^(2)...

Let `f:[-6,6]toR` be defined by `f(x)=x^(2)-3`. Consider the following :
1. `(f^(@)f^(@)f)(-1)=(f^(@)f^(@)f)(1)`
Which of the above is /are correct?

A

1 only

B

2 only

C

Both 1 and 2

D

Neither 1 nor 2

Text Solution

Verified by Experts

The correct Answer is:
C
`f(x)=x^(2)-3`
`fof(x)=f(f(x))=f(x^(2)-3)=(2^(2)-3)^(2)-3`
`=2^(4)-6x^(2)=9-3=x^(4)-6x^(2)+6`
`fof(0)=0-0+6=6`
`f(f(f(x)))=f(x^(4)-6x^(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`
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