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stellarik [79]
3 years ago
5

Plz help!!!

Mathematics
2 answers:
Harman [31]3 years ago
7 0

we know that f(1)=2 so f^-1(2)=1

so B is correct!

Sholpan [36]3 years ago
4 0

Answer:  The correct option is

(B) f^{-1}(x)=\dfrac{1}{x-1}.

Step-by-step explanation:  We are given to select the correct expression that is the inverse of the following function :

f(x)=\dfrac{x+1}{x}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

Let y denotes f(x). Then,

y=f(x)~~~~~~\Rightarrow x=f^{-1}(y).

Substituting this value in equation (i), we get

f(x)=\dfrac{x+1}{x}\\\\\\\Rightarrow y=\dfrac{f^{-1}(y)+1}{f^{-1}(y)}\\\\\\\Rightarrow yf^{-1}(y)=f^{-1}(y)+1\\\\\Rightarrow yf^{-1}(y)-f^{-1}(y)=1\\\\\Rightarrow (y-1)f^{-1}(y)=1\\\\\Rightarrow f^{-1}(y)=\dfrac{1}{y-1}\\\\\Rightarrow f^{-1}(x)=\dfrac{1}{x-1}.

Thus, the required inverse of the given function is

f^{-1}(x)=\dfrac{1}{x-1}.

Option (B) is CORRECT.

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shepuryov [24]

A fisherman can row upstream at 4 mph and downstream at 6 mph. He started rowing upstream until he got tired and then rowed downstream to his starting point. The distance of how far the fisherman row if the entire trip took 2 hours is  9.6 miles

<u />

The speed of an object refers to the change of the object's distance within a specified time.

Mathematically, we can have;

\mathbf{Speed =\dfrac{distance}{time}}

Distance = speed × time

From the information given;

  • The fisherman row upstream for 4 miles/ hour.
  • The distance covered by the fisherman = 4 × t₁  ----- (1)

  • The fisherman row downstream at 6 miles/ hour
  • The distance covered by the fisherman = 6 × t₂  ------ (2)

  • SInce it took the entire trip 2 hours, we can infer that:

  • t₁ + t₂ = 2
  • t₂ = 2 - t₁

From equation (2), replace the above value of t₂ into equation (2)

  • d = 6 t₂
  • d = 6(2 - t₁)
  • d = 12 - 6t₁

From equation (1)

  • d = 4 t₁  

Equation both distance together, we have:

  • 12 - 6t₁ = 4t₁
  • 12 = 4t₁ + 6t₁
  • 12 = 10t₁
  • t₁ = 12/10
  • t₁ = 1.2  hours

From t₂ = 2 - t₁

  • t₂ = 2 - 1.2
  • t₂ = 0.8 hours

From d = 4t₁

Replace t₁ with 1.2 hours

  • d = 4(1.2 hours)
  • d = 4.8 miles

Also, from d = 6t₂

  • d = 6(0.8)
  • d = 4.8 miles

Therefore, we can conclude that the distance of how far the fisherman row if the entire trip took 2 hours is (4.8+4.8) miles = 9.6 miles

Learn more about distance here:

brainly.com/question/12319416?referrer=searchResults

3 0
2 years ago
Write the expression for the perimeter of the rectangle
Sergeu [11.5K]

Answer:

perimeter = 2(x + 5)

this is 2x + 10

x = 55 inches

Step-by-step explanation:

this question is a bit weird because they didn't put the units for 5, so I'm assuming it's in inches...

the perimeter of a rectangle will have two of each, so we can put the 2 outside the bracket since it applies to everything. We have x and we have 5 so put those in the bracket with a plus sign because you add when you're calculating the perimeter.

5 + 5 = 10

120 - 10 = 110 inches (this is 2x)

110 ÷ 2 = 55 inches

4 0
2 years ago
the sum of three numbers is 131. The second of three numbers is seven more than twice the first. The third number is 12 less tha
spin [16.1K]
No. 1 = x
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Answer:

x+(2x+7)+(x-12) = 131

From there you solve to get the numbers:

34, 75 and 22
3 0
3 years ago
One 16 inch pizza serves 4 students how many pizzas are needed for 60 students?​
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Answer:

15 pizzas

Step-by-step explanation:

1 pizza serves 4 students

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60/4=15

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You start baby sitting at 5:30 pm. You babysit for 2 hours. What
Likurg_2 [28]

Answer:

7:30

Step-by-step explanation:

5:30 + 2:00 = 7:30

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