Question 865763
{{{f(x)=x^2-4x+7}}}
{{{g(x)=x-2}}}
{{{f=hg}}}
{{{f=h(x-2)}}}
{{{h(x-2)=(x-2)^2+a(x-2)+b=x^2-4x+7}}}
{{{x^2-4x+4+ax-2a+b=x^2-4x+7}}}
{{{-4x+ax-2a+b=-4x+7}}}
{{{(-4+a)x+(4-2a+b)=-4x+7}}}
Compare the coefficients on the right and left hand sides.
1.{{{-4+a=-4}}}
.
.
{{{4-2a+b=7}}}
2.{{{-2a+b=4}}}
From eq. 1,
{{{a=0}}}
Then,
{{{b=4}}}
.
.
{{{h(x)=x^2+4}}}