Functions Question 466
Question: Let f and g be functions from R To R defined as $ f(x)= \begin{cases} 7x^{2}+x-8,x\le 1 \\ 4x+5,1<x\le 7 \\ 8x+3,x>7 \\ \end{cases} ,g(x)= \begin{cases} | x |,x<-3 \\ 0,-3\le x<2 \\ x^{2}+4,x\ge 2 \\ \end{cases} . . $ Then
Options:
A) $ (fog)(-3)=8 $
B) $ (fog)(9)=683 $
C) $ (gof)(0)=-8 $
D) $ (gof)(6)=427 $
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Answer:
Correct Answer: B
Solution:
[b] we have $ g(-3)=0 $
$ \Rightarrow f(g(-3))=f(0)=7{{(0)}^{2}}+0-8=-8 $
$ \therefore fog(-3)=-8 $ $ g(9)=9^{2}+4=85 $
$ \Rightarrow f(g(9))=f(85)=8.85+3=683 $
$ \therefore fog(9)=683 $ $ f(0)={{7.0}^{2}}+0-8=-8 $
$ \Rightarrow g(f(0))=g(-8)=| -8 |=8 $ $ f(6)=4.6+5=29 $
$ \Rightarrow g(f(6))=g(29)={{(29)}^{2}}+4=845 $
$ \therefore gof(6)=845 $
BETA
