Question

Please can any one please help me with both of these

Answer 1

Question 3:
`4x^3+x^2-12x-3`

Question 4:
`(1)/(2x), x\\eq 0`

Explanation:

Question 3

g(x) * h(x) means to multiply both the functions given.

Also note the distributive property:

`(a+b)(n+p)=an+ap+bn+bp`

Now, lets multiply:

`g(x)*h(x)=(4x+1)(x^2-3)\\=(4x)(x^2)-3(4x)+1(x^2)-1(3)\\=4x^3-12x+x^2-3\\=4x^3+x^2-12x-3`

The 2nd answer choice is right

Question 4

`((f)/(g))(x)` means to divide both the functions and simplify, if possible. Lets do this:

`((f)/(g))(x)=(6x-3)/(12x^2-6x)=(3(2x-1))/(6x(2x-1))=(3)/(6x)=(1)/(2x)`

This is the correct answer.

The restriction on the domain is any x value that we CANNOT PUT IN THE FUNCTION.

We know we cannot divide by 0, so what makes this fraction division by 0??

If we put x = 0, the function is undefined. So x CANNOT be 0.

Third answer choice is right.