All categories

4 years ago

What is the inverse of the functionf(x)=2x+1

1 answer:

7 0

To find the inverse you have steps
1. replace f(x) with y
2. swich x and y places
3. solve for y
4. replace y with f⁻¹(x) (read 'f inverse')

so we have
f(x)=2x+1

replace f(x) with y
y=2x+1

switch x and y
x=2y+1

solve for y
x=2y+1
subtract 1
x-1=2y
divide both sides by 2
$\frac{x-1}{2}$ =y
y= $\frac{x-1}{2}$
repplace y with f⁻¹(x)
f⁻¹(x)= $\frac{x-1}{2}$

You might be interested in

What is the circumference and area of a circle with a radius of 40 inches?

SIZIF [17.4K]

125.6 inches would be the answer. You do 40* 3.14 and you get 125.6, don't forget the units.

5 0

4 years ago

Interpret the regression coefficients. Fill in the blanks below.

bearhunter [10]

Answer:

With the information given in the question, the blank spaces are filled thus:

Step-by-step explanation:

1. The intercept is the estimated amount of a purchase, if time spent viewing the online catalog was zero minutes.

2. The slope coefficient is the estimate of amount that a purchase charges/changes, for one extra minute spent viewing the online catalog.

3. The proportion of total variation in purchases that can be explained by variation in the minutes spent viewing an online catalog is equal to the coefficient of determination.

4. The p-value is the probability value

5. Reject the null hypothesis if there is sufficient evidence to support the claim that the regression slope coefficient is not equal to zero.

NOTE: In the case of number 5, the assumption is that;

Null Hypothesis: The regression slope coefficient = 0

Alternative Hypothesis: The regression slope coefficient ≠ 0

Other answers require numerical information and full data, in order to be computed or calculated.

5 0

3 years ago

The function f(x) = 200 × (1.098)x represents a village's population while it is growing at the rate of 9.8% per year.

AlexFokin [52]

The time for the village to dig the new well is about 7 1/2 years. At this time the population doubles from its current size.

<h3>How to graph a function?</h3>

For a function f(x) = y, the steps to draw a graph for the given function are as follows:

Consider certain values of x
Substitute x values in the given function to obtain y values
Plot the x and y values in the graph
Join the points to know the variation.

<h3>Calculation:</h3>

It is given that,

f(x) = 200 × $(1.098)^x$

Village's population growing rate = 9.8%

Creating a table for x and f(x) values:

x: 0 2 4 6 8 10

f(x = 0) = f(0) = 200 × $(1.098)^0$ = 200

f(x = 2) = f(2) = 200 × $(1.098)^2$ = 241

f(x = 4) = f(4) = 200 × $(1.098)^4$ = 291

f(x = 6) = f(6) = 200 × $(1.098)^6$ = 350

f(x = 8) = f(8) = 200 × $(1.098)^8$ = 423

f(x = 10) = f(10) = 200 × $(1.098)^1^0$ = 509

So,

(x, f(x)): (0, 200) (2, 241) (4, 291) (6, 350) (8, 423) (10, 509)

Plotting these points in the graph and joining the points, the graph is shown below.

Finding the time for the village to dig a new well:

It is given that the population doubled from its current size, the village will need to dig new water well.

The current size of the village = 200

If it doubles for a certain time 't' = 400

So,

400 = 200 × $(1.098)^t$

⇒ $(1.098)^t$ = 2

⇒ log $(1.098)^t$ = log 2

⇒ t log(1.098) = 0.301

⇒ t × 0.04 = 0.301

∴ t = 7.525 years

Therefore, the village's population becomes double at the time 7 and half years from now. So, after 7 1/2 years, the village needs to dig a new well.

Learn more about the function and its graph here:

brainly.com/question/4025726

#SPJ1

3 0

2 years ago

GUYS, I NEED YOUR HELP!! Write an equation for each word problem.

Fofino [41]

Answer:

An apple, potato, and onion all taste the same if you eat them with your nose plugged

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

How to do mean median mode range

murzikaleks [220]

Median is the number in the middle. Here's an example:

1, 2, 3, 4, 5

Just go out in from each end, so we can do:

2, 3, 4

Then do it again until you reach one number.

So 3 is the median. If you have an equal number of numbers, though, this is how you do it:

So your numbers are 1, 2, 3, and 4.

Do the same thing, but then you reach the 2 and the 3 here's what to do:

1. add them together.

2. Divide by two.

So in this example, the median would be:

Mode is the number that repeats itself the most. So like this:

1, 2, 2, 3, 3, 3, 4, 5

The mode is 3, because it repeats itself the most. It isn't 2, because 2 only repeats itself only twice, while 3 repeats itself three times.

Range is the biggest number in the set subtracted by the smallest number. So like this:

1, 2, 3, 4

So we would do:

4-1...

...which is 3. In this set, the range is 3.

Hope I helped!

~Potato

8 0

3 years ago