If f(x) = 2x + 1 and g(f(x)) = 4x^2 + 4x + 3 , find g(x), given that g(x) is in the form of ax^2 + bx + c. How?

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Answer 1 · 2016-12-07T23:38:37

#g(x) = x^2+2#

If #g(x)=a x^2+b x + c# then

#g(f(x))=a (1 + 2 x)^2 + b (1 + 2 x) + c = #
#= 4ax^2+2(b+2a)x+a+b+c#

now comparing coefficients with the target

#g(f(x))=4x^2+4x+3# we have the conditions

#{(a + b + c=3), (4 a + 2 b=4), (4 a=4):}#

obtaining

#a=1,b=0,c=2# so

#g(x) = x^2+2#