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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 2(fog) (7) - (gof) (6) is

A

9

B

11

C

13

D

15

Text Solution

Verified by Experts

The correct Answer is:
A
`(fog)(7)=f(g(7))=f(7^(2)+4)=f(53)`
`=8(53)+3=427`
and `(gof)(6)=g(f(6))=g(4xx6+5)+g(29)`
`=(29)^(2)+4=845`
`therefore 2(fog)(7)-(gof)(6)=2xx427-845=9`
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