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Katen [24]
2 years ago
8

If f(x) and g(x) are polynomial functions, what is the domain of f(x) + g(x) ?

Mathematics
1 answer:
IRINA_888 [86]2 years ago
7 0

Answer:

all real numbers or (-\infty, \infty)

Step-by-step explanation:

since both f(x) and g(x) are polynomials, neither of them have restrictions on their domains. Since they can be defined for all real numbers. It's not like the square root which has a domain of (0, infinity), or log x which is defined only from (0, infinity). So adding these two polynomials would result in a domain of all real numbers.

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Use appropriate algebra and theorem 7. 2. 1 to find the given inverse laplace transform. (write your answer as a function of t.
ollegr [7]

The given function s/(s^2 +3s -4) is proved with the help of inverse Laplace theorem.

According to the statement

we have to find the inverse of the Laplace theorem with the help pf the given theorem in the statement.

So, For this purpose, we know that the

Laplace transformation is a transformation of a function f(x) into the function g(t) that is useful especially in reducing the solution of an ordinary linear differential equation with constant coefficients to the solution of a polynomial equation.

Now, We assume you want to find the inverse transform of s/(s^2 +3s -4).

This can be written in partial fraction form as

\frac{(4/5)}{(s+4)} + \frac{(1/5)}{(s-1)}

which can be found in a table of transforms to be the transform of

\frac{4}{5} e^{-4t} + \frac{1}{5} e^t

There are a number of ways to determine the partial fractions. They all start with factoring the denominator.

s^2 +3x -4 = (s+4)(s-1)

After that, you can postulate the final form and determine the values of the coefficients that make it so.

For example:

\frac{A}{(s+4)}  + \frac{B}{s-1}  = (A+B)s + \frac{(4B-A)}{(s^2 +3x -4)}

This gives rise to two equations:

(A+B) = 1

(4B-A) = 0.

So, The given function s/(s^2 +3s -4) is proved with the help of inverse Laplace theorem.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

Use appropriate algebra and theorem 7.2.1 to find the given inverse laplace transform. (write your answer as a function of t.) ℒ−1 s s2 + 3s − 4.

Learn more about Laplace here

brainly.com/question/11630973

#SPJ4

3 0
2 years ago
Please help me with these questions if you have time
timofeeve [1]

Answer:

Use the following formulas for the tables

Step-by-step explanation:

For the tables given bellow use these formulas for part 7 a and b

y2-y1 over x1-x1

that would give us the slope then plug that into y=mx+b

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Find the number in the proportion <br> 2/12=5/x
Sliva [168]

Answer: x = 30

2/12 x 5/x

(Cross Multiply)

2x = 60

x = 30

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2 years ago
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