Answer to Question #185758 in Discrete Mathematics for zain ul abdeen

Question

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.

Type/Insert your answer here!

Answer 1

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

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

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

$=x^4-40x^2+400+2x^2-40+1=$

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

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

$=(x^2+2x+1)^2-20=$

$=x^4+2x^3+x^2+2x^3+4x^2+2x+x^2+2x+1-20=$

$=x^4+4x^3+6x^2+4x-19$