All categories

4 years ago

Which function is the inverse of function f? f(x)=9x^-12

Mathematics

1 answer:

Svet_ta [14]4 years ago

5 0

Answer:

$(\frac{x}{9})$ ¹²

Step-by-step explanation:

The given function is f(x) = 9x⁻¹²

To find the inverse of f(x) we will write the function in a equation form y = 9x⁻¹²

Now we will replace x from y and y from x

x = 9y⁻¹²

Then we will find the value of y

y⁻¹² = $\frac{x}{9}$

y = $(\frac{x}{9})$ ¹²

Now y will be replaced by f⁻¹(x)

f⁻¹(x) = $(\frac{x}{9})$ ¹²

Therefore inverse of the function f(x) is f⁻¹(x) = $(\frac{x}{9})$ ¹²

You might be interested in

Mr. Smith traveled to a city 300 miles from his home to attend a meeting. Due to car trouble, his average speed returning was 6

Kryger [21]

Answer: The speed at which he traveled to the city is 69.8 mph

Step-by-step explanation:

Let x represent the speed at which he traveled to the city.

Mr. Smith traveled to a city 300 miles from his home to attend a meeting.

Time = distance/speed

Time taken to travel to the city is

300/x

Due to car trouble, his average speed on returning was 6 mph less than his speed going. This means that the speed at which he returned is (x - 6) mph. Time taken to return from the city is

300/(x - 6)

If the total time for the round trip was 9 hours, it means that

300/x + 300/(x - 6) = 9

Cross multiplying by x(x - 6), it becomes

300(x - 6) + 300x = 9x(x - 6)

300x - 1800 + 300x = 9x² - 54x

9x² - 54x - 300x - 300x - 1800 = 0

9x² - 654x -1800 = 0

Applying the general quadratic equation,

x = [- b ± √(b² - 4ac)]/2a

From the equation given,

a = 9

b = - 654

c = 1800

Therefore,

x = [- - 654 ± √(- 654² - 4 × 9 × 1800)]/2 × 9

x = [654 ± √(427716 - 64800)]/18

x = [654 ± √362916.4]/18

x = (654 + 602.4)/2 or x = (654 - 602.4)/18

x = 1256.4/18 or x = 51.6/18

x = 69.8mph or x = 2.9 mph

The speed at which he traveled to the city is 69.8 mph

By checking,

Time spent travelling to the city = 300/69.8 = 4.3 hours

Time spent returning =

300/(69.8 - 6) = 4.7 hours

4.3 + 4.7 = 9 hours

3 0

3 years ago

Square root symbol 640 to the nearest hundreth

Vitek1552 [10]

The square root of 640 is 25.29

5 0

4 years ago

Read 2 more answers

Given the function, check all transformations that occurred from the graph of the function y=x^2

Hatshy [7]

Answer: left 7 units, up 4 units, and vertical compression

Step-by-step explanation:

Given

The function is $y=x^2$

First shift it to the left by 7 units, so the function becomes

$y=(x+7)^2$

Now compress it to make it one-third

$y=\dfrac{1}{3}(x+7)^2$

Now, sift the graph upward by 4 units

$y=\dfrac{1}{3}(x+7)^2+4$

Thus , the conditions are left 7 units, up 4 units, and vertical compression.

4 0

3 years ago

You open a savings account with a beginning balance of $600. You plan on depositing $50 every month until you have enough money

telo118 [61]

Answer:

48 months

Step-by-step explanation:

first take how much you need and add how much you want to leave, so 2500+500=3000. Then delete 600 from 3000, which will give you $2400. divide $2400 by 50 which gives you 48. it will take 48 months to get enough money to purchase a car at $2500 and leave $500 in the account.

8 0

3 years ago

Determine the maximized area of a rectangle that has a perimeter equal to 56m by creating and solving a quadratic equation. What

sveticcg [70]

Answer:

Area of rectangle = $196\,m^2$