Find f∘g and g∘f , where f(x)=x^2+2x+1 and g(x)=x^2-20, are functions from R to R.
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f(x)=x2+2x+1f(x)=x^2+2x+1f(x)=x2+2x+1
g(x)=x2−20g(x)=x^2-20g(x)=x2−20
f∘g=f(x2−20)=(x2−20)2+2(x2−20)+1=f\circ{g}=f(x^2-20)=(x^2-20)^2+2(x^2-20)+1=f∘g=f(x2−20)=(x2−20)2+2(x2−20)+1=
=x4−40x2+400+2x2−40+1==x^4-40x^2+400+2x^2-40+1==x4−40x2+400+2x2−40+1=
=x4−38x2+361=x^4-38x^2+361=x4−38x2+361
g∘f=g(x2+2x+1)=g\circ{f}=g(x^2+2x+1)=g∘f=g(x2+2x+1)=
=(x2+2x+1)2−20==(x^2+2x+1)^2-20==(x2+2x+1)2−20=
=x4+2x3+x2+2x3+4x2+2x+x2+2x+1−20==x^4+2x^3+x^2+2x^3+4x^2+2x+x^2+2x+1-20==x4+2x3+x2+2x3+4x2+2x+x2+2x+1−20=
=x4+4x3+6x2+4x−19=x^4+4x^3+6x^2+4x-19=x4+4x3+6x2+4x−19
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