For which function is f(x) equal to f^-1(x)?

What is the correct answer?

Tasya [4]

Given:

The function is

$f(x)=(x+3)^2(x-5)^6$

To find:

The zeros of the given function.

Solution:

The general form of polynomial is

$P(x)=a(x-c_1)^{m_1}(x-c_2)^{m_2}...(x-c_n)^{m_n}$ ...(i)

where, a is a constant, $c_1,c_2,...,c_n$ are zeros of respective multiplicities $m_1,m_2,...,m_n$ .

We have,

$f(x)=(x+3)^2(x-5)^6$

On comparing this with (i), we get

$c_1=-3,m_1=2$

$c_2=5,m_2=6$

It means, -3 is a zero with multiplicity 2 and 5 is a zero with multiplicity 6.

Therefore, the correct option is B.

5 0

2 years ago

Two numbers whose sum is 44 and whose product is a maximum

Mashcka [7]

Answer:

x = y = 22

Step-by-step explanation:

It would help to know your math course. Do you know any calculus? I'll assume not.

Equations

x + y = 44

Max = xy

Solution

y = 44 - x

Max = x (44 - x) Remove the brackets

Max = 44x - x^2 Use the distributive property to take out - 1 on the right.

Max = - (x^2 - 44x ) Complete the square inside the brackets.

Max = - (x^2 - 44x + (44/2)^2 ) + (44 / 2)^2 . You have to understand this step. What you have done is taken 1/2 the x term and squared it. You are trying to complete the square. You must compensate by adding that amount on the end of the equation. You add because of that minus sign outside the brackets. The number inside will be minus when the brackets are removed.

Max = -(x - 22)^2 + 484

The maximum occurs when x = 22. That's because - (x - 22) becomes 0.

If it is not zero it will be minus and that will subtract from 484

x + y = 44

xy = 484

When you solve this, you find that x = y = 22 If you need more detail, let me know.

4 0

2 years ago

ПОЖАЛУЙСТА ПОМОГИТЕ РЕШИТЬ ДАЮ 23 ОЧКА!!!

posledela

(Простите, пожалуйста, мой английский. Русский не мой родной язык. Надеюсь, у вас есть способ перевести это решение. Если нет, возможно, прилагаемое изображение объяснит достаточно.)

Use the shell method. Each shell has a height of 3 - 3/4 y ², radius y, and thickness ∆y, thus contributing an area of 2π y (3 - 3/4 y ²). The total volume of the solid is going to be the sum of infinitely many such shells with 0 ≤ y ≤ 2, thus given by the integral

$\displaystyle 2\pi \int_0^2 y \left(3-\frac34 y^2\right) \,\mathrm dy = 2\pi \left(\frac32 y^2 - \frac3{16} y^4\right)\bigg|_0^2 = 6\pi$

Or use the disk method. (In the attachment, assume the height is very small.) Each disk has a radius of √(4/3 x), thus contributing an area of π (√(4/3 x))² = 4π/3 x. The total volume of the solid is the sum of infinitely many such disks with 0 ≤ x ≤ 3, or by the integral

$\displaystyle \pi \int_0^3 \left(\sqrt{\frac43x}\right)^2 \,\mathrm dx = \frac{2\pi}3 x^2\bigg|_0^3 = 6\pi$

Using either method, the volume is 6π ≈ 18,85. I do not know why your textbook gives a solution of 90,43. Perhaps I've misunderstood what it is you're supposed to calculate? On the other hand, textbooks are known to have typographical errors from time to time...