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2 years ago

If f(x) = 3x – 15, then f-'(x) =D

Mathematics

1 answer:

tatyana61 [14]2 years ago

5 0

Answer:

$f^{-1}(x)=\frac{x+15}{3}$

$f^{-1}(x)=\frac{x}{3}+5$

Step-by-step explanation:

That means we want to find the inverse function of f(x)=3x-15.

The inverse function is just the swapping of x and y really. We tend to remake the y the subject afterwards.

So we are given:

y=3x-15

First step: Swap x and y

x=3y-15

Now it's time to solve for y.

Second step: Add 15 on both sides:

x+15=3y

Third step: Divide both sides by 3:

(x+15)/3=y

The inverse function is:

$f^{-1}(x)=\frac{x+15}{3}$

You can also split up the fraction like so:

$f^{-1}(x)=\frac{x}{3}+\frac{15}{3}$

The last fraction there can be reduced:

$f^{-1}(x)=\frac{x}{3}+5$

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PLEASE HELP!!!!!

Zielflug [23.3K]

Question #1

Part A:
The y-intercept can be found when x = 0. If you look at your table, when x = 0, y = 5. So the y-intercept is 5.

Part B:
$\sf Slope = \frac{27-5}{1-0} = \frac{22}{1} = \boxed{22}$
The slope is 22.

Part C:
y = mx + b
y = 22x + 5

We are given 225 as the range, or in place of y.
225 = 22x + 5
220 = 22x
x = 10

The domain is 10.

Question #2

Part A:

(2,255)
(5,480)

Standard form is Ax + By = C

$\sf Slope = \frac{y_2-y_1}{x_2-x_1} = \frac{480-225}{5-2} = \frac{255}{3} = \boxed{85}$

Let's plug this into this form first:
$y - y_1 = m(x-x_1)\\\\y -225 = 85(x-2)\\\\y - 225 = 85x - 170\\\\y = 85x + 55$

Now, let's make it into Standard Form.
$y = 85x + 55\\\\y - 85x + 55\\\\ -85x + y = 55\\\\ -1(-85x +y) = -1(55)\\\\\boxed{85x - y = -55}$
What, which is in the box, is your final answer. :)

Part B:
Function notation simply means replacing y with f(x).
We had y = 85x + 55
So your answer is:
$\boxed{f(x) = 85x + 55}$

Part C:
Using the final answer which we got in Part A, we would know that the y-intercept is (0,55) and the x-intercept is (-55/85, 0). We would plot these 2 points, and then draw a line between them. :)

5 0

3 years ago

Joann has a jug containing 128 ounces of milk. She drinks 14 ounces of milk each day. Enter the function f(x) that represents th

Tatiana [17]

Answer:

$f(x)=128-14x$

Step-by-step explanation:

So, we started out with 128 ounces of milk.

Each day, Joann drinks 14 ounces of milk.

Therefore, the amount of milk left over after x days is 14 times x subtracted from 128.

Therefore, our function is:

$f(x)=128-14x$

And we're done!

6 0

3 years ago

A company has 7 male and 9 female employees, and needs to nominate 2 men and 2 women for the company bowling team. How many diff

lys-0071 [83]

Answer:

The team can be formed in 756 different ways

Step-by-step explanation:

This is a combination problem since we are to select a set of people from a group. Combination has to do with selection.

for example, if r number of object is to be selected from a pool of n objects, this can be done in nCr number of ways.

$nCr = \frac{n!}{(n-r)!r!}$

Now If A company has 7 male and 9 female employees, and needs to nominate 2 men and 2 women for the company bowling team, then this can be done in the following way;

$7C2 * 9C2$

$7C2 = \frac{7!}{5!2!} \\= \frac{7*6*5!}{5!*2} \\= 7*3\\= 21ways\\\\similarly;\\\\9C2 = \frac{9!}{7!2!}\\9C2= \frac{9*8*7!}{7!*2} \\9C2 = 9*4\\9C2 = 36$