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
marissa [1.9K]
3 years ago
11

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Mathematics
1 answer:
ddd [48]3 years ago
7 0

Answer:

f'(x) = 4x^2 - 3 for x \le -3

Step-by-step explanation:

See attachment for proper question

Given

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

For

x \ge -3

Required

Determine the inverse function

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

Replace f(x) with y

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

Swap the positions of x and y

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

Multiply both sides by -2

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

-2x =\sqrt{y + 3}

Square both sides

(-2x)^2 =(\sqrt{y + 3})^2

4x^2 =y + 3

Make y the subject

y = 4x^2 - 3

The inverse has been solved. So, we need to replace y with f'(x)

f'(x) = 4x^2 - 3

Next, is to determine the interval

x \ge -3

Change inequality to \le

x \le -3

Hence, the inverse function is:

f'(x) = 4x^2 - 3 for x \le -3

You might be interested in
Divide. 56÷(−23) −54 ​ −59 ​ 59 ​ 54
Vsevolod [243]

Answer:

59/1

Step-by-step explanation:

0 = 0 = 0 = 0 = 0 < 54 < 56 < 59

0 is equal to 0 is equal to 0 is equal to 0 is equal to 0 is less than 54 is less than 56 is less than 59

6 0
3 years ago
Read 2 more answers
Find the y-intercept of the following function:<br><br> <img src="https://tex.z-dn.net/?f=2x%20-%204y%20%3D%209" id="TexFormula1
fomenos

Hi there!

\large\boxed{0, -\frac{9}{4}  }

2x - 4y = 9

Begin by isolating the y variable by moving 2x to the right-hand side of the equation. (Subtract 2x from both sides):

2x - 2x - 4y = 9 - 2x

-4y = 9 - 2x

Further isolate by dividing both sides by -4:

-4y / (-4) = (9 - 2x) / (-4)

y = -9/4 - 2x/(-4)

Simplify further:

y = -9/4 + 1/2x

y = 1/2x - 9/4

The "b" value is the y-intercept, therefore:

x = 0 at y = -9/4

3 0
2 years ago
Read 2 more answers
Select the equation that most accurately depicts the word problem.
Alina [70]

Answer:

:n=95

Step-by-step explanation:

5 0
2 years ago
Sam and Todd went trick-or-treating. When they arrived home and counted their candy, Todd had three times more pieces of candy t
nlexa [21]

Answer:

Step-by-step explanation:

s + t = 544

t = 3s

substitution:

s + 3s = 544

s = 136

t = 3s = 408

Sam has 136 pieces. Todd has 408 pieces.

5 0
3 years ago
For what values of x and y must ABCD be a parallelogram?
Tamiku [17]
X = 7 and Y = 9

Because the parallel sides have to be equal and these inputs make the side equal.
3 0
2 years ago
Other questions:
  • An alloy of tin is 15% tin and weighs 20 pounds. A second alloy is 10% tin How many pounds of the second alloy
    12·1 answer
  • Is the equation y + 1=7(x+2) in point slope form
    8·1 answer
  • Identify the number that does not have the same greatest common factor as the other 368-3420
    6·1 answer
  • Island A is 250 miles from island B. A ship captain travels 260 miles from island A and then finds that he is off course and 160
    15·2 answers
  • What is the volume of the rectangular prism if one side length is 1 2/5 and the other 3 1/3
    12·1 answer
  • How many solutions are there to the system of equations?
    6·2 answers
  • Y = 4x - 2<br> y = x + 3
    8·1 answer
  • Segment MP is a diameter of circle O.
    14·2 answers
  • Determine the slope intercept form of the equation of the line through the given points:
    12·1 answer
  • What is 4^12 x 125^7? Express your answer in scientific notation
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!