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vekshin1
3 years ago
14

Given that f(x)=2x/3 evaluate f^-1(6)

Mathematics
1 answer:
abruzzese [7]3 years ago
4 0

Answer:

9

Step-by-step explanation:

we know by definition that

f^{-1}(f(x))=x\\\\f^{-1}(\frac{2x}{3})=x\\\\f^{-1}(x)=ax\\\\f^{-1}(\frac{2x}{3})=a(\frac{2x}{3})=x\\\\f^{-1}(x)=\frac{3x}{2}

so now we evaluate

f^{-1}(6)=\frac{3*6}{2}\\\\=3*3\\\\f^{-1}(6)=9

and if we want to do an extra step

f^{-1}(f(6))=6\\\\f^{-1}(\frac{2*6}{3})=f^{-1}(4)=\frac{3*4}{2}=6

which works.

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When did the eastern part of the Roman Empire fall?
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The eastern roman empire/ Byzantine Empire fell in 1453. hopefully this helps.
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Pi/6 is the reference angle for:
Ksju [112]
Option B. 13π/6 and Option D. 5π/6

To get the reference angle π/6 for the given angles we will check each angle given in the options.
A. 8π/6
Since 8π/6 means 240° which lies in 3rd quadrant. Therefore reference angle of 240°= 240-180 = 60° or π/3
B. 13π/6
13π/6 means 390° which lies in first quadrant.
Therefore reference angle = 390-360 = 30° or π/6
C. 3π/6
Since 3π/6 means 90° therefore reference angle of 90° is the same as 90°.
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8 0
2 years ago
The clownfish kay wanted to buy for $12 last week has been marked up 8%. What is the new price of the fish?
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4 0
3 years ago
Read 2 more answers
Simplify the expression- <br> 3k+ -9k+ -6+10k
Nady [450]

Answer:

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Step-by-step explanation:

3k+ -9k+ -6+10k=3k-9k-6+10k=4k-6

8 0
3 years ago
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Which inequality matches the given situation if w represents weight in pounds:Baby tigers can be no larger than 4 pounds.
ozzi

Given:

w be the weight in pounds of a baby tigers.

To find:

The inequality if baby tigers can be no larger than 4 pounds.

Solution:

Baby tigers can be no larger than 4 pounds. It mean weight of baby tigers cannot be greater than 4. In other words, the weight of the baby tigers must be less than or equal to 4.

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3 years ago
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