Given that f(x)=x-1 and (g\circ f)(x)=3x^2 + 2, find the function of g in similar form? Thank you

1 Answer
Aug 11, 2018

One possibility is g(x) = 3x^2+6x+5

Explanation:

There are infinite g's which satisfy this condition. Let us consider as g pertaining to the polynomials, for instance let

g(x) = a x^2+b x+c

then

g(f(x)) = a (f(x))^2+b f(x) + c = a(x-1)^2+b(x-1)+c

so

g(f(x)) = (a-3)x^2+(b-2a)x+a+c-b+2 = 3x^2+2

and now comparing coeficients

a = 3, b = 6, c = 5

hence g(x) = 3x^2+6x+5