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3:1 is the answer

it is simplified

Answer:

she will save $32.50 with the monthly pass

Step-by-step explanation:

Answer:

696 steps

Step-by-step explanation:

Answer Before defining the inverse of a function we need to have the right mental image of function.

Consider the function f(x) = 2x + 1. We know how to evaluate f at 3, f(3) = 2*3 + 1 = 7. In this section it helps to think of f as transforming a 3 into a 7, and f transforms a 5 into an 11, etc.

Now that we think of f as "acting on" numbers and transforming them, we can define the inverse of f as the function that "undoes" what f did. In other words, the inverse of f needs to take 7 back to 3, and take -3 back to -2, etc.

Let g(x) = (x - 1)/2. Then g(7) = 3, g(-3) = -2, and g(11) = 5, so g seems to be undoing what f did, at least for these three values. To prove that g is the inverse of f we must show that this is true for any value of x in the domain of f. In other words, g must take f(x) back to x for all values of x in the domain of f. So, g(f(x)) = x must hold for all x in the domain of f. The way to check this condition is to see that the formula for g(f(x)) simplifies to x.

g(f(x)) = g(2x + 1) = (2x + 1 -1)/2 = 2x/2 = x.

This simplification shows that if we choose any number and let f act it, then applying g to the result recovers our original number. We also need to see that this process works in reverse, or that f also undoes what g does.

f(g(x)) = f((x - 1)/2) = 2(x - 1)/2 + 1 = x - 1 + 1 = x.

Letting f-1 denote the inverse of f, we have just shown that g = f-1.

Definition:

Let f and g be two functions. If

f(g(x)) = x and g(f(x)) = x,

then g is the inverse of f and f is the inverse of g.

Exercise 1:

Return to Contents

Finding Inverses

Example 1. First consider a simple example f(x) = 3x + 2.

The graph of f is a line with slope 3, so it passes the horizontal line test and does have an inverse.

There are two steps required to evaluate f at a number x. First we multiply x by 3, then we add 2.

Thinking of the inverse function as undoing what f did, we must undo these steps in reverse order.

The steps required to evaluate f-1 are to first undo the adding of 2 by subtracting 2. Then we undo multiplication by 3 by dividing by 3.

Therefore, f-1(x) = (x - 2)/3.

Steps for finding the inverse of a function f.

Replace f(x) by y in the equation describing the function.

Interchange x and y. In other words, replace every x by a y and vice versa.

Solve for y.

Replace y by f-1(x).

Example 2.  f(x) = 6 - x/2

Step 1 y = 6 - x/2.

Step 2 x = 6 - y/2.

Step 3 x = 6 - y/2.

y/2 = 6 - x.

y = 12 - 2x.

Step 4 f-1(x) = 12 - 2x.

Step 2 often confuses students. We could omit step 2, and solve for x instead of y, but then we would end up with a formula in y instead of x. The formula would be the same, but the variable would be different. To avoid this we simply interchange the roles of x and y before we solve.

Example 3.  f(x) = x3 + 2

This is the function we worked with in Exercise 1. From its graph (shown above) we see that it does have an inverse. (In fact, its inverse was given in Exercise 1.)

Step 1 y = x3 + 2.

Step 2 x = y3 + 2.

Step 3 x - 2 = y3.

(x - 2)^(1/3) = y.

Step 4 f-1(x) = (x - 2)^(1/3).

Exercise 3:

Graph f(x) = 1 - 2x3 to see that it does have an inverse. Find f-1(x). Answer

Step-by-step explanation:

pls brain list

Answer:

The price changed by 92.5 %

Step-by-step explanation:

The regular price of lawn mover = 200 dollars

The new selling price = 85 dollars

Change in selling price = 200 -85 dollars = 115 dollars

% change == [tex]\frac{185}{200} * 100 = 92.5[/tex]

The price changed by 92.5 %

Answer:

the choice shown is correct. A reflection across diagonal BD.

Step-by-step explanation:

Answer:

your right, its A.

Step-by-step explanation:

An 180 rotation would result it with point C being below point A, not making it congruent. A translation is also not possible. A dilation would do nothing. A relfection on the other hand, would make both sides congruent.

Answer:

jjjjjjj

Step-by-step explanation:

nnnnnnn

Answer:

A reflection over the y axis .

Step-by-step explanation:

Given  : Transforms (a,b) to (-a,b).

To find : What type of transformation.

Solution : We have given

Parent function : (a,b) .

Transformed  : (-a ,b).

Transformation rule of reflection over y axis : ( x, y) →→ ( -x ,y).

Then we can say in transformation (a,b) →→→→ (-a,b).

Therefore, A reflection over the y axis

Step-by-step explanation:

plz brain list

Answer:

hes right i took the test

Step-by-step explanation:

Answer: 360 in. squared

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

I did it and got it right

Answer:

1

Step-by-step explanation:

8 + 1 = 9/9

-      -      

9.      9

Given:

The scale on a map is 1:25000.

To find:

How many km on the ground is represented by 6cm on the map?

Solution:

Let x be the km on the ground.

We know that,

1 km = 1000 m

1 m = 100 cm

So,

1 km = 100,000 cm

x km = 100,000x cm

The scale on a map is 1:25000. It means the ratio of map and ground is equal to 1:25000.

[tex]\dfrac{1}{25000}=\dfrac{6}{100,000x}[/tex]

[tex]\dfrac{100,000x}{25000}=6[/tex]

[tex]4x=6[/tex]

[tex]x=\dfrac{6}{4}[/tex]

[tex]x=1.5[/tex]

Therefore, 1.5 km on the ground is represented by 6cm on the map.

Answer:

Roger will have to sleep 2.667 days.

Step-by-step explanation:

If Roger sleeps 3 / 8 of a day in one day.

Then for Roger to sleep the equivalent of one day he will have to sleep

=

Answer:75%

Step-by-step explanation:

To make a fraction into a percent you have to multiply it by 100

So: 15/20 x 100=15x5=75 so he got 75% of his problems right

Answer:

0.25 is a decimal and 25/100 or 25% is the percentage for 2/8.

Step-by-step explanation:

The result is: 0.25 and 25% is 2/8 as a decimal and percent.

Here, we have,

given that,

the fraction is:  2/8

now, we have to write as a decimal and percent.

so, we get,

2/8

[ dividing both numerator and denominator by 2 ]

= 1/4

= 0.25

so, we get, 0.25 is a decimal.

now, we have,

0.25 = 25/100 = 25%

so, we have, 25/100 or 25% is the percentage for 2/8.

To learn more on percentage click:

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Answer:

volume is 17157.28 :)

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

It does not say what the tax is so the answer would be 12. You just divide 2 by 24.

Answer:

12

Step-by-step explanation:

24 divided by 2 is 12 or 2 times 12 is 24

mark me brainliest

Answer:

https://brainly.in/...,..,

Answer:

38.4895cm²

Step-by-step explanation:

area of a circle with r=7

3.142×7² = 153.958

153.958/4 = 38.4895

Answer:

7.7 yards & 14.04 gallons

Step-by-step explanation:

so theres 1.1 yards per meter which can be written out as

1.1 yds/1 meter

multiply that by 7 meters would get you 7.7 yards

same with the punch:

0.26 gallons/ 1 liter times 54 liters = 14.04 gallons

Answer:

August = 3.4

September = 2.8

Step-by-step explanation:

Given

[tex]Total = 6.2\ in[/tex]

Represent August with A and September with S.

So,

[tex]A =S + 0.6[/tex]

Required

Amount of rainfall in each month.

This is calculated using:

[tex]Total = August + September[/tex]

[tex]6.2= A + S[/tex]

Recall that: A = S + 0.6. Substitute

[tex]6.2= S + 0.6 + S[/tex]

[tex]6.2= 2S + 0.6[/tex]

Collect Like Terms

[tex]2S = 6.2 - 0.6[/tex]

[tex]2S =5.6[/tex]

Solve for S

[tex]S = 5.6/2[/tex]

[tex]S = 2.8[/tex]

Substitute 2.8 for S in [tex]A =S + 0.6[/tex]

[tex]A = 2.8 + 0.6[/tex]

[tex]A = 3.4[/tex]

Answer:

It's a total increase by 27,65%

Step-by-step explanation:

1,11 × 1,15 = 1,2765

1,2765 = +27,65%

Answer:

B

Step-by-step explanation:

Answer:

4x-20

Step-by-step explanation:

Answer:

Step-by-step explanation: