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Liono4ka [1.6K]
3 years ago
7

Find the inverse of the function.

Mathematics
2 answers:
worty [1.4K]3 years ago
8 0

f(x) = 4\sqrt[3]{x} - 8

Let's replace f(x) with y

y = 4\sqrt[3]{x} - 8

Switch the x and y

x = 4\sqrt[3]{y} - 8

Now, let's solve for y. Start off by adding 8 to both sides.

x + 8 = 4\sqrt[3]{y}

Divide both sides by 4

\frac{x}{4}  + 2 = \sqrt[3]{y}

Take each side by the power of 3

(\frac{x}{4} + 2)^{3} = y

Now, let's replace y with f^{-1}(x)

f^{-1}(x) = (\frac{x}{4} + 2)^{3} is the inverse

skad [1K]3 years ago
7 0

Answer:

x3 over 64+3x^ over 8+3x+8

Step-by-step explanation:

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x and x+19

Step-by-step explanation:

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4 0
3 years ago
Given the parent function, y=2^x, write an equation for a function that has a vertical shift down 5 units.
Ulleksa [173]

Answer:

y=2^x - 5

Step-by-step explanation:

"- 5" demonstrates a verical shift 5 units down

5 0
3 years ago
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3 0
3 years ago
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You have 976 grams of a radioactive kind of rhodium. How much will be left after 120 seconds if its half-life is 30 seconds?
erik [133]

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Step-by-step explanation:

5 0
2 years ago
An oval track is made by erecting semicircles on each end of a 60m by 120m rectangle. Find the length of the track and the area
vodomira [7]
Refer to the figure shown below.

Because the question states that the semi circles are at the ends of the rectangle, each semicircle has a radius of 30 m.

The circumference of the oval is
2π(30) + 2*120 = 60π + 240 m = 428.5 m

The area of the oval is 
π(30²) + 60*120 = 900π + 7200 m² = 1.0027 x 10⁴ m²

Note:
If the semi circles are placed on the 120-m sides of the rectangle, then similar calculations yield:
Circumference = 120π + 120 m = 497 m
Area = 3600π + 7200 m² = 1.851 x 10⁴ m²

Answer:
If the semi circles are placed on the 60-m sides of the rectangle, then
Circumference = 60π + 240 m, or 428.5 m
Area = 900π + 7200 m², or 1.0027 x 10⁴ m²

if the semi circles are placed on the 120-m sides of the rectangle, then
Circumference = 120π + 120 m, or 497 m
Area = 3600π + 7500 m², or 1.851 x 10⁴ m²


3 0
4 years ago
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