Gatebook Test

Question

Comments

-9

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Given is 3

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given that g(x)=$1-x+x^{2}$ and f(x)=$ax+b$

then (gof)(x)= g(ax+b) =

$1-ax-b+a^{2}x^{2}+b^{2}+2abx= 9x^{2}-9x+3$

$a^{2}x^{2}+(2ab-a)x+(b^{2}-b+1)=9x^{2}-9x+3$

Then

$a=\pm 3 $ and $b=2,-1$

Answer 1

$(gof)(x) = g(f(x)) = g(ax+b) $

$= 1 - ax -b + (ax+b)^2 $

$= 1 - ax -b + (ax)^2 + b^2 + 2$

 

$a^2x^2+(2ab−a)x+(b2−b+1)=9x^2−9x+3$

Then  $a=±3$ and $b=2,−1$