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
Alex777 [14]
2 years ago
14

Find the inverse of the given function. f(x) = -1/2√x + 3, x ≥ -3

Mathematics
2 answers:
shepuryov [24]2 years ago
5 0

Answer:

The inverse of the function is f^{-1}(x)=4x^2-3, for x\leq 0

Step-by-step explanation:

Given : Function f(x)=-\frac{1}{2}\sqrt{x+3}

To find : The inverse of the given function?

Solution :  

To find the inverse of the function we replace the value of x and y and then find y in terms of x which is the inverse of the function.

Let f(x)=y

y=-\frac{1}{2}\sqrt{x+3}                

Replace the value of x and y.

x=-\frac{1}{2}\sqrt{y+3}                  

Now, we solve in terms of x the value of y

-2x=\sqrt{y+3}  

(x must be negative)

Squaring both side,

(-2x)^2=(\sqrt{y+3})^2  

4x^2=y+3  

4x^2-3=y  

So, The inverse of the function is f^{-1}(x)=4x^2-3, for x\leq 0

inna [77]2 years ago
4 0
<span>Find the inverse of the given function.

f(x) = -1/2√x + 3, x ≥ -3

I will have to assume that you meant f(x) = -(1/2)sqrt(x) + 3.  If you actually meant f(x) = -(1/2)sqrt(x+3), then obviously the correct result would be different.

1.  Replace "f(x)" by "y:"  y </span>= -(1/2)sqrt(x) + 3
 2.  Interchange x and y:  x = -(1/2)sqrt(y) + 3
3.  Solve for y:  x-3=-(1/2)sqrt(y), so that 2(3-x)= sqrt(y) and y=+sqrt(2[3-x])
4.  Replace "y" with 

           -1
        f      (x) = sqrt(2[3-x])

Here, there are restrictions on x, since the domain of the sqrt function does not include - numbers.  The domain here is (-infinity,3]
You might be interested in
A delivery to the flower shop is recorded in the chart above. The shop makes centerpiece arrangements using 36 flowers that are
Alchen [17]

Answer:

yes, they will be able to make at least 10 arrangements using each type of flower

no, they will not be able to make 100 arrangements using each type of flower.

Step-by-step explanation:

Explain your thinking: The shop makes arrangements with only the same type of flower. We know that each arrangement requires 36 flowers. By analyzing the data, we can see how many arrangements they can make based on each flower type.

There are 580 tulips - and we need 36 per arrangement

580/36= 16 arrangements of tulips

There are 2,410 daisies

2410/36= 66 arrangements of daisies

There are 4,000 carnations

4,000/36= 111 arrangements of carnations.

Since there are at least 10 arrangements per set of flowers, the first statement is true (we CAN make at least 10 arrangements using each type of flower)

Since there is only 16 arrangements for tulips and 66 for daisies, we CANNOT have at least 100 arrangements per flower type

3 0
3 years ago
(1+i)^2(x+yi)=4+5i<br> Solve for x and y
faust18 [17]

Answer:

x = 5/2

y = -2

Step-by-step explanation:

(1+i)² (x+yi) = 4+5i

(1+2i+i²)(x+yi) = 4+5i

(1+2i-1)(x+yi) = 4+5i

2i(x+yi) = 4+5i

2i²y + 2xi = 4+5i

-2y + 2xi = 4 + 5i

By comparing both sides,

-2y = 4

y = -2,

2x = 5

x = 5/2

7 0
2 years ago
Factorise fully 12x - 8​
mestny [16]

Answer:

4(3x-2)

Step-by-step explanation:

Have a great day :)

5 0
2 years ago
Read 2 more answers
Sixteen is divided by the sum of a number q and 1
atroni [7]

No context. If you want us to write an expression:

16 / (q+1)

4 0
2 years ago
What does this graph tell you about the price of almonds?
liraira [26]

Answer:

<h2>2.3 pound costs 45 cents</h2>

Step-by-step explanation:

That point on the graph shows it. $0.45 for the cost, 2.3 for the pounds.

I'm always happy to help :)

7 0
3 years ago
Read 2 more answers
Other questions:
  • 5. Molly subscribed to a new streaming service. The monthly cost includes a $9 base fee plus $0.50 for each
    8·1 answer
  • allison has 5 times as many baseball cards as football cards.in all,she has 120 baseball and football cards.how many baseball ca
    5·2 answers
  • Identify the constant term in this expression.
    12·1 answer
  • A right triangle has side lengths a, b, and c as shown below.
    6·1 answer
  • Question 1. Find h (-2)
    7·2 answers
  • What is the length of line segment KJ?
    10·1 answer
  • Can you help me please ​
    5·1 answer
  • Mell ordered 3 times as many hamburgers as cheeseburgers, and four more orders of french fries than cheeseburgers. There were a
    12·2 answers
  • A vector starts at point ( -3, 8) and ends at point (-2, 2) what is the horizontal component of the vector?
    14·2 answers
  • What is the measure of m? 6 3 n 18 m = [?] Give your answer in simplest form. Enter​
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!