Figuring out coefficients of composition of a first

Erik Cantu

Erik Cantu

Answered question

2022-04-05

Figuring out coefficients of composition of a first degree polynomial into a quadratic
Given: g(x)=x2+x2 and gf=2[2x25x+2], find f(x)(f(x) is form ax+b)

Answer & Explanation

clarkchica44klt

clarkchica44klt

Beginner2022-04-06Added 17 answers

A more easy way is the following:
If f(x)=ax+b, then
gf(x)=(ax+b)2+(ax+b)2=a2x2+(2ab+a)x+(b2+b2)
By identification, you must have a2=4,2ab+a=10 and b2+b2=4. If a=2, you obtain b=3 which works; if a=2, you obtain b=2 which also works. So you have two solutions:
f(x)=2x3  and  f(x)=2x+2

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