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butalik [34]
4 years ago
6

Gracie read 150 pages of a book she got for her birthday the book is 227 pages long whats the right equation

Mathematics
1 answer:
Yakvenalex [24]4 years ago
7 0
Are there options or when is her birthday what is the rest of the problem
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A function f has the following verbal description: multiply by 3, add 5, and
STALIN [3.7K]

Regarding the functions in this problem, it is found that:

a) The verbal description of the inverse is: Take the third root, subtract by 5 and divide by 3.

b) The formulas are:

  • f(x) = (3x + 5)³.
  • f^{-1}(x) = \frac{\sqrt[3]{x} - 5}{3}

c) The compositions result in x, hence they are inverses.

<h3>How to obtain the inverse function?</h3>

The original function is described as follows:

  • Multiply by 3: 3x.
  • Add 5: 3x + 5.
  • Take the third power: (3x + 5)³.

Hence the function is:

y = (3x + 5)³.

To obtain the inverse functions, we exchange x and y and then isolate y, hence:

x = (3y + 5)³

\sqrt[3]{x} = \sqrt[3]{(3y+5)^3}

3y + 5 = \sqrt[3]{x}

3y = \sqrt[3]{x} - 5

y = \frac{\sqrt[3]{x} - 5}{3}

f^{-1}(x) = \frac{\sqrt[3]{x} - 5}{3}

The verbal description of the inverse is:

  • Take the third root. sqrt[3](x).
  • Subtract by 5: sqrt[3](x) - 5.
  • Divide by 3.

The compositions are given as follows:

  • f(f^{-1}(x)) = f\left(\frac{\sqrt[3]{x} - 5}{3}\right) = \left(3\left(\frac{\sqrt[3]{x} - 5}{3}\right + 5)\right)^3 = (\sqrt[3]{x})^3 = x
  • f^{-1}(f(x)) = f^{-1}((3x + 5)^3) = \frac{\sqrt[3]{(3x + 5)^3} - 5}{3} = \frac{3x + 5 - 5}{3} = x

More can be learned about inverse functions at brainly.com/question/11735394

#SPJ1

4 0
2 years ago
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