Question

I NEED HELP ASAP PLEASEEEE

Answer 1

`(f-g)(x)=x^2-6x+5` dom: (-∞,∞)

`((f)/(g))(x)=x-7+(7)/(x+2)` dom: (–∞,–2)u(–2,∞)

Explanation:

`(f-g)(x)=f(x)-g(x)=(x^2-5x+7)-(x+2)` *distribute the negative sign into (x+2)!

`x^2-5x+7-x-2\\x^2-6x+5`

a parabola (anything that begins with
`x^2`) will have a domain of (-∞,∞) or all real numbers!!

`((f)/(g) )(x)= (x^2-5x+7)/(x+2)` use synthetic division to divide (the attached picture)

domain: Because the graph is not continuous, you have to write the domains on both sides of the asymptote which is (-∞,-2)u(-2,∞)

synthetic division:

1. take the divisor (x+2) and solve for x. x= –2 this goes in the top left corner

2. write the numbers AND their signs on the top row. if there is no number and just the variable (like
`x^2` ) just write 1.

3. the first number gets pulled down

4. multiply -2 by 1 and subtract it from –5. (-5-2= -7)

multiply -2 by -7 and add that to the next number in the top row which is -7. (-7 + 14=7)

5. the first number in the bottom row of numbers is the first number in the answer but with one less exponent than the dividend. **write 1 as x**

6. the last number in the bottom row, if it is not 0, is a remainder. write it as that number over the divisor. in this case the remainder is 7. so write it as
`(7)/(x+2)`