Question

please answer the question on the screenshot below, also please explain to me how you got your answer.

Answer 1

QUESTION 1

The given functions are;

`f(x)=5x^2-2x` and
`g(x)=5x^2+x-4`

`(f+g)(x)=f(x)+g(x)`

`(f+g)(x)=5x^2-2x+3x^2+x-4`

We regroup like terms to obtain;

`(f+g)(x)=5x^2+3x^2-2x+x-4`

This simplifies to;

`(f+g)(x)=8x^2-x-4`

The correct answer is A.

QUESTION 2

The given functions are;

`f(x)=3x^2+5` and
`g(x)=x-2`.

`(fg)(x)=(f(x))(g(x))`

This implies that;

`(fg)(x)=(3x^2+5)(x-2)`

`\Rightarrow (fg)(x)=3x^3-6x^2+5x-10`

The correct answer is B.

QUESTION 3

The given functions are

`f(x)=3x^2+10x-8` and
`g(x)=3x^2-2x`.

`((f)/(g))(x)=(f(x))/(g(x))`

`((f)/(g))(x)=(3x^2+10x-8)/(3x^2-2x),x\\e0,(2)/(3)`

We factor to obtain;

`((f)/(g))(x)=((x+4)(3x-2))/(x(3x-2)),x\\e0,(2)/(3)`

We cancel the common factors to obtain;

`((f)/(g))(x)=(x+4)/(x),x\\e0,(2)/(3)`

The correct answer is A.