I am unsure how to do this, is it possible someone could give me a step by step guide so I can have a good understanding of it.
f(x) and g(x) are defined over the real number set R as follows: $g(x) = 1-x+x^2$ and $f(x) = ax + b$. if $g(f(x)) = 16x^2-12x+3.$ determine all the possible values of a and b.
Hint: Start by plugging the expression for $f$ into the expression for $g$. That is, simplify the expression $g(ax+b)=1-(ax+b)+(ax+b)^2$. Then set this equal to $16x^2-12x +3$.