If f(x)=2x^2 +4 and g(x)=x-3,which number satisfies f(x)=(f•g) (x)

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17-10-2015
Mathematics

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If f(x)=2x^2 +4 and g(x)=x-3,which number satisfies f(x)=(f•g) (x)

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konrad509 konrad509 · Answer 1 · 2015-10-17T22:30:37+02:00

konrad509 konrad509

17-10-2015

[tex](f\cdot g)(x)=f(x)\cdot g(x)\\\\ (f\cdot g)(x)=(2x^2+4)(x-3)\\ (f\cdot g)(x)=2x^3-6x^2+4x-12\\\\ 2x^2+4=2x^3-6x^2+4x-12\\ 2x^3-8x^2+4x-16=0\\ 2x^2(x-4)+4(x-4)=0\\ (2x^2+4)(x-4)=0\\ 2(x^2+2)(x-4)=0\\ \boxed{x=4}[/tex]

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