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3 years ago

The _ _, f(x) = x, is formed by the composition of a function and its inverse. (2 words)

Mathematics

1 answer:

jonny [76]3 years ago

8 0

Answer:

Identity function

Step-by-step explanation:

We are given the following in the question:

Let f(x) be a function.

Then, inverse of f(x) can be written as:

$f^{-1}(x)$

The composition function of the function and the reverse function can be found as:

$(f\circf^{-1})(x) = f(f^{-1})(x) = x$

which is an identity function.

Thus, the correct answer is

The identity function, f(x) = x, is formed by the composition of a function and its inverse.

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3. You want to have $4000 in your savings account after 2 years. Find the amount you should deposit for each of the situations d

pychu [463]

Answer:

Part A)

About $3767.34.

Part B)

About $3692.47.

Step-by-step explanation:

Part A)

Recall that compound interest is given by the formula:
$\displaystyle A = P\left(1+\frac{r}{n}\right)^{nt}$

Where A is the final amount, P is the initial amount, r is the interest rate, n is the number of times compounded per year, and t is the number of years.

To obtain $4000 after two years, let A = 4000 and t = 2.

Because the account pays 3% interest compounded monthly, r = 0.03 and n = 12.

Substitute and solve for P:

$\displaystyle \begin{aligned} (4000) & = P\left(1+\frac{(0.03)}{(12)}\right)^{(12)(2)} \\ \\ P & = \frac{4000}{\left(1+\dfrac{(0.03)}{(12)}\right)^{(12)(2)}} \\ \\ & \approx \$3767.34\end{aligned}$

In concluion, about $3767.34 should be deposited.

Part B)

Recall the formula for continuous compound:

$\displaystyle A = Pe^{rt}$

Where e is Euler's number.

Hence, let A = 4000, r = 0.04 and t = 2. Substitute and solve for P:

$\displaystyle \begin{aligned}(4000) & = Pe^{(0.04)(2)} \\ \\ P & = \frac{4000}{e^{(0.02)(4)}} \\ \\ & \approx \$3692.47 \end{aligned}$

In conclusion, about $3692.47 should be deposited.

8 0

2 years ago

Can you solve this for me

jenyasd209 [6]

The number in the blank box should be 44 because it said that "3 times x and 4 times y is 44".

You need to multiply the first equation by 3:

3x + 3y = 39.

Then, subtract the first equation from the second equation:

3x - 3x = 0

4y - 3y = y

44 - 39 = 5

Your new equation should look like this: y = 5

Now, substitute y = 5 into the first original equation:

x + 5 = 13

x = 8

Ans. (x, y) = (8, 5)

4 0

3 years ago

1. When solving the equation: 8n -2 = 1 +n + 5 + 6, Response area could NOT be the first step that would yield a solution

Hatshy [7]

Answer:

n = 2

Step-by-step explanation:

8 0

3 years ago

PLZ NEED A PROFESSIONAL :( Which is the equation of a parabola with a directrix at y = 2 and a focus at (5, 0)

inysia [295]

Answer:

Answer D (the fourth one)

Step-by-step explanation:

First, we need to set up a (y−k)^2=4p(x−h). After plugging in all of your values, you would get (x-5)^2=-4(y-1). Now, we need to solve in terms of y by dividing each side by the factors that don't contain the variable. Your final solution should be $y = -\frac{1}{4}(x - 5^{2}) + 1$