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xz_007 [3.2K]
1 year ago
5

Given r(x) = startfraction 11 over (x minus 4) squared endfraction , which represents a domain restriction on r(x) and the corre

sponding inverse function?.
Mathematics
1 answer:
Dmitry_Shevchenko [17]1 year ago
3 0

The domain and inverse of the function

r(x) = \frac{11}{(x - 4)^2} is

Domain = \mathbb{R} - \{4\},

r^{-1}(x) = \pm \sqrt{\frac{11}{x}} + 4

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

The given function is

r(x) = \frac{11}{(x - 4)^2}

r(x) is not defined if x - 4 = 0

r(x) is not defined for x = 4

Domain = \mathbb{R} - \{4\},

Where \mathbb{R} is the set of all real number

Let r(x) = y

\frac{11}{(x-4)^2} = y\\(x - 4)^2 = \frac{11}{y}\\x - 4 = \pm \sqrt{\frac{11}{y}}\\x = \pm\sqrt{\frac{11}{y}}  +4

<em />r^{-1}(x) = \pm \sqrt{\frac{11}{x}} + 4

To learn more about function, refer to the link:

brainly.com/question/22340031

#SPJ4

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Bumek [7]

Answer:

Step-by-step explanation:

let y represent number of years...

9 ft tall = (12 * 9) = 108 inches

10 ft tall = (12 * 10) = 120 inches

Type A : 9 ft (or 108 inches) and grows 6 inches per year..

108 + 6y

Type B : 10 ft (or 120 inches) and grows 3 inches per yr

120 + 3y

how many years will it take them to be the same height...so when will they be equal....so set them equal and solve for y

108 + 6y = 120 + 3y

6y - 3y = 120 - 108

3y = 112

y = 112/3

y = 37 1/3 years....or 37 years and 4 months <====

check...

108 + 6(37 1/3) = 120 + 3(37 1/3)

108 + 6(112/3) = 120 + 3(112/3)

108 + 672/3 = 120 + 336/3

672/3 - 336/3 = 120 - 108

336/3 = 112

112 = 112 (correct)

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C) None of the above

The transformation is not a reflection because the image is not an exact reflection. It is a little bit tilted.

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The transformation is not a translation because the image was altered in some way, by being tilted.

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8 ABC please trig assignment
Papessa [141]

Using equivalent angles, the solutions are given as follows:

a) x = \frac{15\pi}{23}.

b) x = \frac{9\pi}{62}, x = \frac{53\pi}{62}.

c) x = \frac{3\pi}{8}, \frac{11\pi}{8}

<h3>What are equivalent angles?</h3>

Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.

For item a, we have to find the equivalent angle on the 2nd quadrant, where the sine is also positive.

Hence:

\pi - \frac{8\pi}{23} = \frac{23\pi}{23} - \frac{8\pi}{23} = \frac{15\pi}{23}

Hence x = \frac{15\pi}{23}.

For item b, if two angles are complementary, the sine of one is the cosine of the other.

Complementary angles add to 90º = 0.5pi, hence:

x + \frac{11\pi}{31} = \frac{\pi}{2}

x = \frac{31\pi}{62} - \frac{22\pi}{62}

x = \frac{9\pi}{62}

The equivalent angle on the second quadrant is:

\pi - \frac{9\pi}{62} = \frac{62\pi}{62} - \frac{9\pi}{62} = \frac{53\pi}{62}

Hence the solutions are:

x = \frac{9\pi}{62}, x = \frac{53\pi}{62}

For item c, the angles are also complementary, hence:

x + \frac{\pi}{8} = \frac{\pi}{2}

x = \frac{4\pi}{8} - \frac{\pi}{8}

x = \frac{3\pi}{8}

The tangent is also positive on the third quadrant, hence the equivalent angle is:

x = \pi + \frac{3\pi}{8} = \frac{8\pi}{8} + \frac{3\pi}{8} = \frac{11\pi}{8}

Hence the solutions are:

x = \frac{3\pi}{8}, \frac{11\pi}{8}

More can be learned about equivalent angles at brainly.com/question/28163477

#SPJ1

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