Let f and g be real valued functions def...

Let `f` and `g` be real valued functions defined as
`f(x)={{:(7x^(2)+x-8",",xle 1),(4x+5",",1lt x le 7),(8x+3",",x gt7):} " " g(x)={{:(|x|",",xlt -3),(0",",-3le x lt 2),(x^(2)+4",",xge 2):}`
The value of `gof (0) + fog (-3)` is

A

a) -8

B

b) 0

C

c) 8

D

d) 16

Verified by Experts

The correct Answer is:

B

`(gof)(0)=g(f(0))=g(7(0)^(2)+0-8)`
`=g(-8)=|-8|=8`
and `(fog)(-3)=f(g(-3))=f(0)=7(0)^(2)+0-8=-8`
`therefore (gof)(0)+(fog)(-3)=-8+8=0`

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