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
levacccp [35]
3 years ago
5

I need help with number 4

Mathematics
2 answers:
ss7ja [257]3 years ago
7 0

Answer:  Choice D

f^{-1}(x) = (x-3)^2+2\\\\

============================================================

Explanation:

First we replace f(x) with y. This is because both y and f(x) are outputs of a function.

To find the inverse, we swap x and y and solve for y like so

y = \sqrt{x-2}+3\\\\x = \sqrt{y-2}+3 \ \text{ .... swap x and y; isolate y}\\\\x-3 = \sqrt{y-2}\\\\(x-3)^2 = y-2 \ \text{ ... square both sides}\\\\(x-3)^2+2 = y\\\\y = (x-3)^2+2\\\\f^{-1}(x) = (x-3)^2+2\\\\

Note: because the range of the original function is y \ge 3, this means the domain of the inverse is x \ge 3. The domain and range swap roles because of the swap of x and y.

As the graph shows below, the original and its inverse are symmetrical about the mirror line y = x. One curve is the mirror image of the other over this dashed line.

AnnyKZ [126]3 years ago
5 0

Answer:

D

Step-by-step explanation:

let y = f(x) and rearrange making x the subject

y = \sqrt{x-2} + 3 ( subtract 3 from both sides )

y - 3 = \sqrt{x-2} ( square both sides )

(y - 3)² = x - 2 ( add 2 to both sides )

(y - 3)² + 2 = x

Change y back into terms of x with x = f^{-1} (x) , then

f^{-1} (x) = (x - 3)² + 2 → D

You might be interested in
The surface area of the figure
kirza4 [7]
525cm bro because i just took it right now

4 0
3 years ago
tank contains 20002000 liters​ (L) of a solution consisting of 112112 kg of salt dissolved in water. Pure water is pumped into t
Ganezh [65]

Answer:

Answer:

t ≅ 5.09 min

Step-by-step explanation:

we have that if in 4000 L/sol there is 132 kg salt and the pumping speed is 12L/s, we must find how much of salt is pumping per second and then find the amount of salt remaining

12L/s*132kg salt/4000L = 0.396 Kg salt/s,  this means that 0.396 kg per second comes out , It should be found that the amount of salt must be drained so that only 11 kg of salt remain

132kg salt - 11 kg salt = 121 kg salt, so

121Kg salt*s/0.396Kg salt ≅ 305.55 s ⇒ 305.55s*min/60s ≅ 5.09 min

Step-by-step explanation:

6 0
4 years ago
The graph shows the amount of money paid when purchasing bags of peanuts at the zoo:
I am Lyosha [343]

Answer:

$4

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
You use a line of best fit for a set of data to make a prediction about an unknown value. the correlation coeffecient is -0.833
alina1380 [7]

Answer: The square root of π has attracted attention for almost as long as π itself. When you’re an ancient Greek mathematician studying circles and squares and playing with straightedges and compasses, it’s natural to try to find a circle and a square that have the same area. If you start with the circle and try to find the square, that’s called squaring the circle. If your circle has radius r=1, then its area is πr2 = π, so a square with side-length s has the same area as your circle if s2  = π, that is, if s = sqrt(π). It’s well-known that squaring the circle is impossible in the sense that, if you use the classic Greek tools in the classic Greek manner, you can’t construct a square whose side-length is sqrt(π) (even though you can approximate it as closely as you like); see David Richeson’s new book listed in the References for lots more details about this. But what’s less well-known is that there are (at least!) two other places in mathematics where the square root of π crops up: an infinite product that on its surface makes no sense, and a calculus problem that you can use a surface to solve.

Step-by-step explanation: this is the same paragraph The square root of π has attracted attention for almost as long as π itself. When you’re an ancient Greek mathematician studying circles and squares and playing with straightedges and compasses, it’s natural to try to find a circle and a square that have the same area. If you start with the circle and try to find the square, that’s called squaring the circle. If your circle has radius r=1, then its area is πr2 = π, so a square with side-length s has the same area as your circle if s2  = π, that is, if s = sqrt(π). It’s well-known that squaring the circle is impossible in the sense that, if you use the classic Greek tools in the classic Greek manner, you can’t construct a square whose side-length is sqrt(π) (even though you can approximate it as closely as you like); see David Richeson’s new book listed in the References for lots more details about this. But what’s less well-known is that there are (at least!) two other places in mathematics where the square root of π crops up: an infinite product that on its surface makes no sense, and a calculus problem that you can use a surface to solve.

5 0
3 years ago
100 points
nikitadnepr [17]

Answer:

Step-by-step explanation:

√3(√6+√15)

3√2+3√5

2√3+3√5

3√7

3√2+9√5

7 0
2 years ago
Other questions:
  • Is 5.29 less than or greater than 52.9
    5·2 answers
  • Prove that sin3a-cos3a/sina+cosa=2sin2a-1
    11·2 answers
  • Find the slope intercept form of the equation that passes through the given point and is parallel to the given line (-3,2) and y
    9·1 answer
  • Can you help me to put it in order please
    5·1 answer
  • PLEASE HELP ME ASAP<br> PLEASE
    13·1 answer
  • Select all of the true statements about the standard deviation of a quantitative variable. The standard deviation of a set of va
    11·1 answer
  • What is the range of these numbers: 79 72 78 -71 -91 65
    6·2 answers
  • Turn, Aklo earns 8 points. On his second turn, he loses 3 points.
    7·1 answer
  • Which figure is a radius of F? worth 20 points
    5·2 answers
  • How do you solve number 5?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!