Question

Given f(x)=x^3+2x^2 and g(x)=3x^2-1,find the following and state their domains.

a)f+g

b)f-g

c)fg

d)f/g

Answer 1

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Answer 2

`f(x)+g(x)=x^3+2x^2+3x^2-1=x^3+5x^2-1\\ D:x\in\mathbb{R}`


`f(x)-g(x)=x^3+2x^2-(3x^2-1)=x^3+2x^2-3x^2+1=x^3-x^2+1\\ D:x\in\mathbb{R}`


`f(x)\cdotg(x)=(x^3+2x^2)(3x^2-1)=3x^5-x^3+6x^4-2x^2=\\ 3x^5+6x^4-x^3-2x^2\\ D:x\in\mathbb{R}`


`(f(x))/(g(x))=(x^3+2x^2)/(3x^2-1)\\ 3x^2-1\\ot=0\\ 3x^2\\ot=1\\ x^2\\ot=(1)/(3)\\ x\\ot =-(\sqrt3)/(3) \wedge x\\ot =(\sqrt3)/(3)\\ D:x\in(-\infty,-(\sqrt3)/(3) )\cup((\sqrt3)/(3) ,\infty)`