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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 4(gof) (2) - (fog) (9) is

A

0

B

2

C

5

D

9

Text Solution

Verified by Experts

The correct Answer is:
D
`(gof)(2)=g(f(2))=g(4xx2+5)=g(13)`
`=(13)^(2)+4=173`
and `(fog)(g)=f(g(9))=f(9^(2)+4)=f(85)`
`=8xx85+3=683`
`therefore 4(gof)(2)-(fog)(9)=4xx173-683=9`
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