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Pachacha [2.7K]
2 years ago
8

Find the inverse of the Function

0-4" id="TexFormula1" title="f(x)=\sqrt[3]{\frac{x}{9} } -4" alt="f(x)=\sqrt[3]{\frac{x}{9} } -4" align="absmiddle" class="latex-formula">

Mathematics
1 answer:
scoray [572]2 years ago
6 0

9514 1404 393

Answer:

  D

Step-by-step explanation:

Solve x = f(y) for y.

  x = ∛(y/9) -4

  x +4 = ∛(y/9) . . . . . add 4

  (x +4)³ = y/9 .. . . . . cube

  9(x +4)³ = y . . . . . . multiply by 9

The inverse function is ...

  f⁻¹(x) = 9(x +4)³ . . . . . matches the last choice

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Write the equation of a line perpendicular to 9xplus7yequals6 that passes through the point ​(9​,negative 7​).
andrew11 [14]

k:\ y=m_1x+b_1\\\\l:\ y=m_2x+b_2\\\\k\ ||\ l\iff m_1=m_2\\\\k\ \perp\ l\iff m_1m_2=-1

We have:

k:\ 9x+7y=6\ \ \ |-9x\\\\7y=-9x+6\ \ \ \ |:7\\\\y=-\dfrac{9}{7}x+\dfrac{6}{9}\to m_1=-\dfrac{9}{7}\\\\l:\ y=m_2x+b\\\\l\ \perp\ k\iff-\dfrac{9}{7}m_2=-1\ \ \ \ |\cdot\left(-\dfrac{7}{9}\right)\\\\m_2=\dfrac{7}{9}\to\ l:\ y=\dfrac{7}{9}x+b

We know. The line <em>l</em> passes throught the point (9, -7). Substitute the coordinates of the poin to the equation of line<em> l </em>:

-7=\dfrac{7}{9}\cdot9+b\\\\-7=7+b\ \ \ \ |-7\\\\b=-14

y=\dfrac{7}{9}x-14\ \ \ \ |\cdot9\\\\9y=7x-126\ \ \ \ |-9y\ |+126\\\\7x-9y=126

Answer: y=\dfrac{7}{9}x-14\to7x-9y=126


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PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!!
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The last option is the answer. You can double check by substituting the -3 for the x values and the 17 for y values and the statements would be true.

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Page 1 = D

Page 2 = D

Step-by-step explanation:

Hope that helps!

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