1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
marta [7]
3 years ago
13

Find f^(-1)for the function f(x)= (1)/(x+2)

Mathematics
1 answer:
Artyom0805 [142]3 years ago
3 0

If f(x) and f^{-1}(x) are inverses of each other, then we have

f\left(f^{-1}(x)\right) = x

Since f(x) = \frac1{x+2}, we have

f\left(f^{-1}(x)\right) = \dfrac1{f^{-1}(x)+2} = x

Solve for f^{-1}(x) :

\dfrac1{f^{-1}(x)+2} = x \\\\ 1 = x\left(f^{-1}(x)+2\right) \\\\ 1 = x f^{-1}(x) + 2x \\\\ x f^{-1}(x) = 1 - 2x \\\\ f^{-1}(x) = \dfrac{1-2x}x \\\\ \boxed{f^{-1}(x) = \dfrac1x - 2}

(provided that <em>x</em> ≠ 0 and <em>x</em> ≠ -2)

You might be interested in
Kevin draws a figure that has four sides.All sides have the same length.His figure has no right angles.What figure does Kevin dr
svetoff [14.1K]
Rhombus or diamond I think. I hope that this helps!
5 0
2 years ago
What is the expanded form for 602,050,123
Fudgin [204]
600000000+2000000+50000+100+20+3
3 0
2 years ago
Solve the system of equations using elimination<br> x-y=3<br> 2x+2y=50
pishuonlain [190]

Answer:

X=14

Y=11

Step-by-step explanation:

14-11=3

14x2=28

11x2=22

22+28=50

Hope that works :)

6 0
2 years ago
Read 2 more answers
Please help!!
oksano4ka [1.4K]
1. -6 ≤ x < -1 . . . . conjunction
2. x ≤ 6 . . or . . 10 ≤ x . . . . disjunction
3. 7 ≤ x < 12 . . . . conjunction
4. x < -9 . . or . . -3 ≤ x . . . . disjunction
5. 2 ≤ x ≤ 5 . . . . conjunction
6. x ≤ 54 . . or . . 66 ≤ x . . . . disjunction
7. 39 < x ≤ 43 . . . . conjunction

_____
Your problem statement provided no letters.
8 0
3 years ago
Read 2 more answers
Jason had $32. He spent all the money on buying 4 CDs for $x each and 2 magazines for $y each. If Jason had bought 5 CDs and 2 m
Leni [432]
You can set up two equations from the information given. I will set them up for you:

32 = 4x + 2y
36 = 5x + 2y

Let's solve the first equation to come up with a value for y.

32 = 4x + 2y
32 - 4x = 2y
16 - 2x = y

Now we plug y into the other equation.

36 = 5x + 2(16-2x)
36 = 5x + 32 - 4x
4 = x

Now we have our real x value and we can plug it into the first equation.

32 = 4(4) + 2y
32 = 16 + 2y
16 = 2y
8 = y

Since x = 4 and y = 8, you get the final coordinates of (4,8).

Your answer is the second statement provided above.
3 0
2 years ago
Other questions:
  • What is the y-intercept of the function f(x) = -2/9x+1/3?<br>A _2/9<br>B -1/3<br>C 1/3<br>D 2/9​
    14·1 answer
  • Alice's bank account balance is -$35, and Sarah's is -$23.
    14·1 answer
  • The students in a class of 24 share 48 apple slices and 36 orange slices equally among them. How many pieces of fruit did each s
    13·1 answer
  • Choose 2 axioms that allows 22 + (m + 8) to be written as m + 30
    9·2 answers
  • F(x)=(−x−2)(−2x−3) find the first solution and then the second
    11·1 answer
  • Simpfly by dividing [-5/8] divided by [-3/4]
    7·1 answer
  • In the diagram, PQ and ST are parallel lines. Find the value of x.<br><br>please help!!​
    13·1 answer
  • What’s the answer for 3(4w +5)
    7·2 answers
  • I NEED HELP PLEASE!!!!,!,!,!
    12·1 answer
  • Para las celebraciones del barrio de Santiago se junto cierta cantidad de dinero que se distribuirá de la siguiente forma:?
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!