Question #6a9e1

1 Answer
Feb 7, 2018

Given

# f(x)=x^2-7x+18 #

When #f(x)=8# we get

#x^2-7x+18 =8#

#=>x^2-7x+10=0#

#=>x^2-5x-2x+10=0#

#=>x(x-5)-2(x-5)=0#

#=>(x-5)(x-2)=0#

#=>x=5and2#

So when #f(x)=8# then #x=5and2#

Hence #g(f(x))=2x+3# will give two values of #g(8)# for #x=5 and 2#

So
When #x=5#
#g(8)=2*5+3=13#

And
When #x=2#
#g(8)=2*2+3=7#

Hence the sum of all possible values of g(8) is #13+7=20#