Question #185758

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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Expert's answer
2021-05-07T09:41:41-0400

f(x)=x2+2x+1f(x)=x^2+2x+1

g(x)=x220g(x)=x^2-20


fg=f(x220)=(x220)2+2(x220)+1=f\circ{g}=f(x^2-20)=(x^2-20)^2+2(x^2-20)+1=

=x440x2+400+2x240+1==x^4-40x^2+400+2x^2-40+1=

=x438x2+361=x^4-38x^2+361


gf=g(x2+2x+1)=g\circ{f}=g(x^2+2x+1)=

=(x2+2x+1)220==(x^2+2x+1)^2-20=

=x4+2x3+x2+2x3+4x2+2x+x2+2x+120==x^4+2x^3+x^2+2x^3+4x^2+2x+x^2+2x+1-20=

=x4+4x3+6x2+4x19=x^4+4x^3+6x^2+4x-19


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