Find the inverse of each function

1. f(x) = 4/(x+2) - 2

2. f(x)= -2x^5 - 3

Answers

Answer 1

9514 1404 393

Answer:

  1. f^-1(x) = 4/(x+2) -2

  2. f^-1(x) = (-(x+3)/2)^(1/5)

Step-by-step explanation:

1. As with all "inverse function" problems, solve for y:

  x = f(y)

  x +2 = 4/(y +2) . . . . add 2

  y +2 = 4/(x +2) . . . . . multiply by (y+2)/(x+2)

  y = 4/(x+2) -2 . . . . . subtract 2

We see that this function is its own inverse. The attached graph shows it is symmetrical about the line y=x.

  f^-1(x) = 4/(x+2) -2

__

2. x = f(y)

  x +3 = -2y^5 . . . . add 3

  -(x +3)/2 = y^5 . . . . . divide by 2

  (-(x +3)/2)^(1/5) = y . . . . take the 5th root

  f^-1(x) = (-(x +3)/2)^(1/5)

In typeset form, that is ...

  [tex]\displaystyle f^{-1}(x)=\sqrt[5]{\frac{-(x+3)}{2}}\\\\\text{or}\\\\f^{-1}(x)=-\frac{1}{2}\sqrt[5]{16x +48}[/tex]

This last version is with the denominator "rationalized" and the contents of the radical "simplified." It may be a preferred form.

_____

The graphs show the function and inverse are symmetrical about the line y=x, as they should be.

Find The Inverse Of Each Function1. F(x) = 4/(x+2) - 22. F(x)= -2x^5 - 3
Find The Inverse Of Each Function1. F(x) = 4/(x+2) - 22. F(x)= -2x^5 - 3

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(NO LINKS)

Answers

Given:

The figure of a right angle triangle with hypotenuse 10 and two angles [tex]45^\circ, 90^\circ[/tex]

To find:

The lengths of the legs.

Solution:

Two angles are given. By using the angle sum property, the third angle is:

Third angle = [tex]180^\circ-45^\circ- 90^\circ[/tex]

                   = [tex]45^\circ[/tex]

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Let x be the lengths of both legs. Then by using Pythagoras theorem, we get

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Step-by-step explanation:

Answer:

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Answer:

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Step-by-step explanation:

Answer:

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hope this helps and hope you get a good score on your assignment/test/quiz

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answers

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Answers

Answer:

At the end of the month she has $578

Step-by-step explanation:

Given

[tex]Start\ balance = 600[/tex]

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[tex]Withdrawal: 100; 20; 100[/tex]

Required

The balance at month end

Deposits simply means adding cash to the account and it has a very simple interest. So, we add .

While Withdrawal taking money out of the account. So, we subtract.

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Answers

Answer:

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Step-by-step explanation:

area of rectangle

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area of circle

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subtract

112-50.27 = 61.73

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Answer:

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Step-by-step explanation:

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Answer:

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Answers

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

Radius = 26 yards.

Step-by-step explanation:

The complete rotation of the sprinkler makes a circle of radius R (R is the length of the stream of water).

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Answer:

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Step-by-step explanation:

Answer:

[tex]8,400in^2[/tex]

Step-by-step explanation:

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Answers

Answer

$266.66

Step-by-step explanation:

We have here ,

Principal = $200 Rate = 16% Time = 10 months = 10/12 yrs.

We can use the formula of SI to calculate the SI . After adding it to principal we will get the amount .

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