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satela [25.4K]
3 years ago
10

9.10' is how many times as large as 3. 10%

Mathematics
1 answer:
GrogVix [38]3 years ago
8 0
6 is the. possible answer
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If f(x)=x^3-x+2, then (f^-1)'(2)
yawa3891 [41]

Note that f(x) as given is <em>not</em> invertible. By definition of inverse function,

f\left(f^{-1}(x)\right) = x

\implies f^{-1}(x)^3 - f^{-1}(x) + 2 = x

which is a cubic polynomial in f^{-1}(x) with three distinct roots, so we could have three possible inverses, each valid over a subset of the domain of f(x).

Choose one of these inverses by restricting the domain of f(x) accordingly. Since a polynomial is monotonic between its extrema, we can determine where f(x) has its critical/turning points, then split the real line at these points.

f'(x) = 3x² - 1 = 0   ⇒   x = ±1/√3

So, we have three subsets over which f(x) can be considered invertible.

• (-∞, -1/√3)

• (-1/√3, 1/√3)

• (1/√3, ∞)

By the inverse function theorem,

\left(f^{-1}\right)'(b) = \dfrac1{f'(a)}

where f(a) = b.

Solve f(x) = 2 for x :

x³ - x + 2 = 2

x³ - x = 0

x (x² - 1) = 0

x (x - 1) (x + 1) = 0

x = 0   or   x = 1   or   x = -1

Then \left(f^{-1}\right)'(2) can be one of

• 1/f'(-1) = 1/2, if we restrict to (-∞, -1/√3);

• 1/f'(0) = -1, if we restrict to (-1/√3, 1/√3); or

• 1/f'(1) = 1/2, if we restrict to (1/√3, ∞)

6 0
2 years ago
Find the 12th term in the following arithmetic sequence
sattari [20]
It is going up by 5 so i believe your answer would be 57
4 0
3 years ago
Convert 12 1/2 to a percent
kompoz [17]

Answer:

12 and a half to a percent IS 1250%

Step-by-step explanation:

You have to multiply 12.5 by 100

5 0
3 years ago
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ILL GIVE BRAINLIEST IF CORRECT
castortr0y [4]

Answer:

B. 18x3 + 6x2 + 14x - 72

6 0
3 years ago
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Which of the following statements must be true based on the diagram below select all that apply
ipn [44]

Answer:

all are true other than NONE OF THE ABOVE

Step-by-step explanation:

Hope this helps. let me know if any questions.

3 0
2 years ago
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