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aalyn [17]
3 years ago
11

If f(x) and f^-4(x) are inverse functions of each other and f(x) = 2x+5, what is f^-1(x)?

Mathematics
1 answer:
miss Akunina [59]3 years ago
4 0

For this case we must find the inverse of the following function:

f (x) = 2x + 5

Then, we follow the steps:

We change f (x)by y:

y = 2x + 5

We exchange the variables:

x = 2y + 5

We clear the variable "y":

x-5 = 2y\\y = \frac {x-5} {2}

We change y for f^{-1}(x):

f^{-1}(x) = \frac {x-5} {2}

Answer:

f^{-1}(x) = \frac {x-5} {2}

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Solve the right triangle. Will give points!
Anna [14]

Answer:

  • EF = 4.1
  • DE = 9.1
  • m∠F = 66°

Step-by-step explanation:

The hypotenuse and one acute angle are given. The relevant relations are ...

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

__

For the given triangle, these tell us ...

  sin(24°) = EF/DF = EF/10

  EF = 10·sin(24°) ≈ 4.1

and ...

  cos(24°) = DE/DF = DE/10

  DE = 10·cos(24°) ≈ 9.1

The remaining acute angle is the complement of the given one:

  F = 90° -D = 90° -24°

  ∠F = 66°

6 0
2 years ago
16. Two golfers completed one round of golf. The first golfer had a score
bearhunter [10]

9514 1404 393

Answer:

  9

Step-by-step explanation:

The extra shots can be computed from the difference in their scores:

  6 -(-3) = 6 +3 = 9

The first golfer took 9 more shots.

6 0
3 years ago
An economy pack of highlighters contains 12 yellow, 6 blue, 4 green, and 3 orange highlighters. An experiment consists of random
Serhud [2]

Answer:

The probability of choosing a blue or yellow highlighter when one yellow highlighter is picked is 17/25.

Step-by-step explanation:

Here, according to the question:

Total number of yellow highlighters  = 12

Total number of blue  highlighters  = 6

Total number of green highlighters  = 4

Total number of orange  highlighters  = 3

So, the total number of highlighters  =  12 + 6 + 4 + 3  = 25

Let E1 : Event of selecting a yellow highlighter.

P(E1)  = \frac{\textrm{Total number of yellow highlighters}}{\textrm{Total Highlighters}}  = \frac{12}{25}

Let E2 : Event of selecting blue or yellow highlighter ONCE yellow highlighter is selected.

So, the total yellow highlighters left after selecting one = 12 -1  = 11

Also, the number of blue highlighter  =  6

So, the TOTAL FAVORABLE options to E2 = 6+ 11 = 17

P(E2)  =

\frac{\textrm{Total number of yellow  + Blue   highlighters}}{\textrm{Total Highlighters}} = \frac{17}{25}

Hence, the probability that a blue or yellow highlighter is selected given that a yellow highlighter is selected is 17/25.

7 0
3 years ago
the average speed of a race car is 240 km/h. if the race is 200 laps long with each lap being 4.02 km, how long will the race la
shtirl [24]
Each lap = 4.02 km
 200 laps x 4.02 = 804 km total

804 km / 240 km/h = 3.35 hours = 3 hours and 21 minutes

7 0
3 years ago
Haruka owns an umbrella factory. The revenue, RRR, she makes from selling nnn umbrellas is given by the function R(n)=18nR(n)=18
Levart [38]

<u>Answer:</u>

E(n) = n + 5


<u>Explanation:</u>

The profit is the difference between the amount of money received as a revenue and the amount of money spent as expenses.

<u>This means that:</u>

Profit = Revenue - Expenses


<u>Rearrange the formula to solve for the expenses, we get:</u>

Expenses = Revenue - Profit


<u>We are given that: </u>

Revenue = R(n) = 18n

Profit = P(n) = 17n - 5


<u>Substitute in the above formula to get the formula for expenses as follows:</u>

E(n) = R(n) - P(n)

E(n) = 18n - (17n-5)

E(n) = 18n - 17n + 5

E(n) = n + 5


Hope this helps :)

5 0
3 years ago
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