Mathematics, 18.09.2019 20:40 rosieposie27

If f(x) = x^2 - 81 and
g(x) = (x - 9)^-1 ( x + 9)
find g(x) x f(x)
a. (x+9)^2
b. (x-9)^2
c. 2(x-9)
d. (x+9)(x-9)
i know how to set this up, i just don't understand how to do it with two parenthesis on the g(x) side and the -1 exponent is throwing me off, provide a brief explanation including what the -1 does .

Answers: 1

Show answers

Answers

Since I'm on my phone, I can't write the solution in LaTeX, but I can try to explain the approach as best as I can.

We are given two separate functions, namely f(x) and g(x). Since f(x) is a difference of two squares (x^2 is a squared term and 81 is a squared term), we can rewrite it as (x + 9)(x - 9).

Now, this will help us when we multiply through by g(x). Let's discuss the solution to g(x). In exponent laws, any number to the power of a negative number will be reciprocated. That is, the function will turn into fractional notation.

Example: Rewrite x^-1 in positive index form.

Since the power is negative, we will need to reciprocate x^1 to get 1/(x^1).

Example: Rewrite 3x^-2 in positive index form.

Since the x term is only affected by the power, the 3 is left unchanged and stays on the numerator. Now, since the power is negative, we need to reciprocate x^2 to yield: 3/(x^2).

Using the same process, we can rewrite g(x) as being (x + 9)/(x - 9).

Now, we want f(x) * g(x) so that becomes:

(x + 9)(x - 9) *(x + 9)/(x - 9)

(x - 9) cancels in the numerator and denominator to yield: (x + 9)^2

Answer from: Quest

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2:

(2 x^3 + 7 x^2 + (x + 4 x) + 2)/(x (x + 2))

x + 4 x = 5 x:

answer: (2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

Answer from: Quest

[2, 2.5)

(2.5, 3]

step-by-step explanation:

i think its these two not sure [2, 2.5)

(2.5, 3]

Another question on Mathematics

Mathematics, 21.06.2019 20:30

Barbara has a good credit history and is able to purchase a car with a low-interest car loan. she co-signs a car loan for her friend jen, who has poor credit history. then, jen defaults on the loan. who will be held legally responsible by the finance company and why? select the best answer from the choices provided. a. barbara will be held legally responsible because she has a good credit history. b. jen will be held legally responsible because she drives the car. c. barbara will be held legally responsible because she is the co-signer. d. jen will be held legally responsible because she has a poor credit history. the answer is a

Answers: 3

Answer

Mathematics, 21.06.2019 22:30

What fraction is equivalent to 0.46464646··· a. 46⁄999 b. 46⁄100 c. 46⁄99 d. 23⁄50

Answers: 1

Answer

Mathematics, 21.06.2019 22:30

Explain how you could use the interactive table to tell if sets of points are on the same line. math 8

Answers: 2

Answer

Mathematics, 22.06.2019 00:00

Can someone me with this graph problem by the way i need to know the answers by today since this assignment is due ! !