Question

Please can any one please help me with both of these

Answer 1

Answer:

Question 3:  $4x^3+x^2-12x-3$

Question 4:  $\frac{1}{2x}, x\neq 0$

Step-by-step 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

$(\frac{f}{g})(x)$  means to divide both the functions and simplify, if possible. Lets do this:

$(\frac{f}{g})(x)=\frac{6x-3}{12x^2-6x}=\frac{3(2x-1)}{6x(2x-1)}=\frac{3}{6x}=\frac{1}{2x}$

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.