Mathematics College

Let f(x) = x+2/x+6
f^-1(-6) =

Answers

Answer 1

We can explicitly find the inverse. If [tex]f^{-1}(x)[/tex] is the inverse of [tex]f(x)[/tex], then

[tex]f\left(f^{-1}(x)\right) = \dfrac{f^{-1}(x)+2}{f^{-1}(x)+6} = x[/tex]

Solve for the inverse :

[tex]\dfrac{f^{-1}(x) + 2}{f^{-1}(x) + 6} = x[/tex]

[tex]\dfrac{f^{-1}(x) + 6 - 4}{f^{-1}(x) + 6} = x[/tex]

[tex]1 - \dfrac4{f^{-1}(x) + 6} = x[/tex]

[tex]1 - x = \dfrac4{f^{-1}(x) + 6}[/tex]

[tex]f^{-1}(x) + 6 = \dfrac4{1-x}[/tex]

[tex]\implies f^{-1}(x) = \dfrac4{1-x} - 6[/tex]

Then when x = -6, we have

[tex]f^{-1}(-6) = \dfrac4{1-(-6)} - 6 = \dfrac47-6 = \boxed{-\dfrac{38}7}[/tex]

Alternatively, we can first solve for x such that [tex]f(x) = -6[/tex]. Then taking the inverse of both sides, [tex]x = f^{-1}(-6)[/tex]. (The difference in this method is that we don't compute the inverse for all x.)

We have

[tex]\dfrac{x+2}{x+6} = -6[/tex]

[tex]x + 2 = -6 (x + 6)[/tex]

[tex]x + 2 = -6x - 36[/tex]

[tex]7x = -38[/tex]

[tex]\implies x = \boxed{-\dfrac{38}7}[/tex]

Related Questions

What do you add to 17/4 to make 5?

Answers

The number that can be added to 17/4 to make 5 is 3/4

How to add fractions

Given

Add to 17/4 to make 5

let

x = number added

x + 17/4 = 5

x = 5 - 17/4

x = (20-17) / 4

x = 3/4

Learn more about fraction:

https://brainly.com/question/11562149

What is that answer Share 126 gallons of petrol between Steve and Dave in the ratio 2:5

Answers

5+2=7 parts in the ratio
126÷7=18 gallons per part
s:d
18x2:18x5
36:90

LAST ATTEMPT IM MARKING AS BRAINLIEST!! (Pythagorean theorem )

Answers

Answer:

x = √7km

Step-by-step explanation:

Answer:

Step-by-step explanation:

You take a right triangle and find the lengths of the two sides that are vertical and horizontal. Then, using the formula a^2 + b^2 = c^2, find the length of C

(aka: Hypotenuse)

hope this helps!

PLEASE HELP
no linkss

Answers

Answer:

-5.2, -4.75, -9/2

Step-by-step explanation:

From least to greatest it is -5.2, -4.75, -9/2

A recipe calls for 2 tsp of oatmeal to make 7 protein bars.
How much oatmeal is needed to bake 27 protein bars?

A) 3 1/3 tsp
B) 9 tsp
C) 21 tsp
D) 81 tsp

Answers

Answer:

3 1/3 is the answer im pretty sure

A flagpole has a 10 foot shadow. A soldier standing next to it is 6 foot tall and has a 2 foot shadow. How tall is the flagpole?

Answers

Answer:

30 feet tall flag pole

Step-by-step explanation:

ratio
a. L
b. bozo
d. your life is bad
c. ratio again

Answers

Answer:

Step-by-step explanation:

The Answer is d for sure

Which of the following are possible side
lengths for a triangle?
A. 8, 5, 7
B. 10, 3, 7
C. 9,5, 15

Answers

Answer:

A yes B No C Yes

Step-by-step explanation:

The length of the third side is greater than the difference and less than the sum of the two smallest sides.

8, 5, 7 Using the 5 and 7 the third side is > (7 - 5) and < (5 + 7)

the third side is > 2 and < 12 so 8 is OK

10, 3, 7 Use the two smallest number: 3 and 7

the third side is > (7 - 3) and < (3 + 7)

the third side is > 4 and < 10 No it is 10

9, 5, 15 Use the two smallest number 9, 5

the third side is > (9 - 5) and < (9 + 5)

the third side is > 4 and < 14 Yes

Answer:

A. 8, 5 , 7

Step-by-step explanation:
the other guy who answered gave two yes's so I chose one and A. was correct.

Increase £26 by 30%
Increase £440 by 19%
Decrease £62 by 20%
Decrease £300 by 48%

Answers

Step-by-step explanation:

standard deviation of $3

Find a 98% confidence interval about the mean (one decimal place).

Is a value of X=48 unusually high or is it normal? Choose correct explanation

f (x) = 2log
(1/4x-5) +6
Find the Inverse

f-1(x) = 120.52–3 + 20
f-1(x) = 4.30.53–6 +5
f-1(x) = 4.30.52–3 + 20
-6
=
=

Answers

Answer:

6 is the answer for the question

Help help help help help math

Answers

Step-by-step explanation:

don't panic. just breathe and think logically.

why would these angles be different ? how could they be different ?

right : they cannot be different. otherwise the 2 horizontal lines would not be parallel.

so, yes, indeed, these 2 angles are identical.

3x + 2 = 2x + 6

x = 4

that's it.

At a dinner, the meal cost $22 and a sales tax of $1.87 was added to the bill.
How much would the sales tax be, in dollars and cents, on a $66 meal?

Answers

The sales tax for a $66 meal would be $5.61.

Bob spends $650 for a gym membership plus $75 for each hour with a personal trainer. Is the description linear or exponential?

Answers

Answer:

y = 75x + 650

So I think it's linear.

4x+3y=7 what is the coefficients

Answers

co-efficient of x is 4co-efficient of y is 3constant term is -7

nasa pick po yong sagot

#CARRYONLEARNING

loveuall:)

help me please ill mark as the brainiest if correct.

Answers

Answer:

14 minutes

Step-by-step explanation:

For every two minutes the temperature increases by 15 c. since 8 equals 55, 10 is 70, 12 is 85, and 14 is 100.

Answer:

Step-by-step explanation:

LAST ATTEMPT !! MARKING AS BRAINIEST!!

Answers

Answer: You have to get a better picture cause I cant see but D'C is 8

Step-by-step explanation:

Which of the following statements about the image below is true?

Answers

Answer:

d. Line UR and Line VW are parallel

Step-by-step explanation:

If they were to continue going straight, they would not touch, making them parallel.

I hope this helps!

Every week Jim runs 8 miles and bikes 12 miles. Write an ordered pair to represent how many miles Jim runs and bikes in 5 weeks. Use the drop-down menus to complete the sentence. Jim runs Choose... miles and bikes Choose... miles in 5 weeks. The ordered pair would be Choose... .

Answers

The ordered pair to represent how many miles Jim runs and bikes in 5 weeks is (3.33, 5)

Writing an ordered pair to represent how many miles Jim runs and bikes in 5 weeks.

From the question, we have the following parameters that can be used in our computation:

Every week Jim runs 8 miles and bikes 12 miles.

This means that we have the ratio

Run : Bike = 8 miles : 12 miles

When he bikes for 5 weeks, we have

Run : 5 weeks = 8 miles : 12 miles

This gives

Run/5 weeks = 8/12

So, we have

Run = 5 weeks * 8/12

Evaluate the products

Run = 3.33 weeks

Hence, the number of weeks is 3.33 and the ordered pair is (3.33, 5)

Answers

ANSWER: 12
Ok done. Thank to me :>

Interest = $45.58, time = 1 year, rate = 2.25%. Find the principal. Round to the nearest hundredth place

Answers

Answer:

$2,025.78

Step-by-step explanation:

I = Prt ⇒ P = [tex]\frac{I}{rt}[/tex]

2.25% = 0.0225

P = 45.58 ÷ ( 0.0225 × 1 ) ≈ $2,025.78

Multiply and fill in the blanks
a) 5pq(p2+ q2+pq)
b) -7pr (pq – qr - rq)
c) (4x-3y) (5x-4a)

with explanation pls !

Answers

The solution to the simplification of the algebraic expressions are;

A) 5p³q + 5pq³ + 5p²q

B) 14pqr² - 7p²qr

C) 20x² - 15xy - 16ax + 12ay

A) We have the expression;

5pq(p² + q² + pq)

Multiplying out using the concept of distributive property, we have;

(5pq × p²) + (5pq × q²) + (5pq × pq)

>> 5p³q + 5pq³ + 5p²q

B) We have the expression;

-7pr(pq – qr - rq)

Multiplying out using the concept of distributive property, we have;

-7p²qr + 7pqr² + 7pqr²

>> 14pqr² - 7p²qr

C) (4x - 3y)(5x - 4a)

By quadratic expansion, we have;

(4x * 5x) - (3y * 5x) - (4x * 4a) + (4a * 3y)

>> 20x² - 15xy - 16ax + 12ay

Read more about simplification of algebra at; https://brainly.com/question/4344214

PLEASE HELPPPPP
Write the equation of the circle in standard form from the given information. Show all work.
Center (0,0)
Diameter = 14

Answers

The answer is x^2 + y^2 = 49

solve for x where xe(0,2pi). state exact answers.
b)
[tex] \frac{1}{ \sqrt{3} } \sin(2x) + \cos(x) = 0[/tex]
e)
[tex]3 \cos(x) + \tan(x) = 0[/tex]
Note: for question e, get this equation to a point ready for factoring or to use the quadratic formula, then stop. make sure its in standard form.

Answers

Answer:

that's the correct answer

Solve the inequality for x.
9x - 7 < 7x - 25

Answers

Answer:

x<-9

Step-by-step explanation:

subtract the 7x from the right side to bring it over to the left side to get:

2x-7<-25

then add the 7 from the left side to bring it over to the right side to get:

2x<-18 and then divide both sides by 2 to get the final inequality to be:

x<-9

Answer: x < -9Step-by-step explanation:9x - 7 < 7x - 25=> 9x - 7x < 7 - 25=> 2x < -18=> x < -9Conclusion:

Therefore, the solved inequality is x < -9.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

If Amari had 15 apples and 14 got taken away how many would there be??

Answers

Answer:

15-14=1

Step-by-step explanation:

1 apple left

Answer:

1 apple

Step-by-step explanation:

15-14=1

Hope the helps!

5x + y = 11
3x − y = 9

Answers

Answer:

x = 5/2y = -1.5

Step-by-step explanation:

5x + y = 11

3x − y = 9

=> 5x + y = 11

+3x − y = +9

=> 8x = 20

=> x = 20/8

=> x = 5/2

=> 5(5/2) + y = 11

=> 25/2 + y = 11

=> 12.5 + y = 11

=> y = 11 - 12.5

=> y = -1.5

Therefore, the answers are:

x = 5/2y = -1.5

Hoped this helped.

[tex]BrainaicUser1357[/tex]

What functions have a range of {y £ R | -

Answers

Answer:

the second and the fourth have a range of real no

what is 2*6 i need help

Answers

Its 12 for answer

Step-by-step explanation:

2×6=12

Travis has hired Charlie and Dora to plant flowers. Dora can plant 150 flowers in the same time it takes Charlie to plant 120 flowers, which can be shown using the following relationship where d and c are the respective rates at which Dora and Charlie can plant flowers:

150 over d equals 120 over c

Also, Dora can plant 18 flowers more per day than Charlie.

How many flowers can Charlie plant per day?

Answers

Answer:

Step-by-step explanation:

If the rates d and c are flowers per day, we have ...

150/d = 120/c

d -c = 18

Multiplying the first equation by cd/30, we have ...

5c = 4d

Multiplying the second equation by 4 gives ...

4d -4c = 72

Adding these equations together, we get ...

5c +4d -4c = 4d +72

Simplifying and subtracting 4d leaves ...

c = 72

Charlie can plant 72 flowers per day.

HELP! ( MATH )
WILL GIVE BRAINILEST!

Question:
Graph the solution of the equation.
b – 5 = –8

Answers

Answer:

b = -3 so A is answer

good luck

Answer:

option C is the correct answer

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Let f(x) = x+2/x+6 f^-1(-6) =

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Let f(x) = x+2/x+6
f^-1(-6) =