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
Marianna [84]
3 years ago
9

Which is the inverse of the function f(x) = x2 − 4?

Mathematics
1 answer:
Rudiy273 years ago
7 0

The function is not one-to-one function, hence the inverse doesn't exist for the whole domain of the function. But if we restrict the domain to x\in(-\infty,0] or x\in[0,\infty), then we can give the inverse.

f(x)=x^2-4\\\\y=x^2-4\\\\x^2=y+4\\\\x=\sqrt{y+4} \vee x=-\sqrt{y+4}\\\\f^{-1}(x)=\sqrt{x+4}\vee f^{-1}(x)=-\sqrt{x+4}

So, when D_{f(x)}:x\in(-\infty,0], the inverse is f^{-1}(x)=-\sqrt{x+4} and when D_{f(x)}:x\in[0,\infty), the inverse is f^{-1}(x)=\sqrt{x+4}.

You might be interested in
Can somebody help me alive this?
Sveta_85 [38]

Answer:6/4

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Which of these are arithmetic sequences?
Leviafan [203]

Answer:

D

Step-by-step explanation:

The first and last sequence have a common difference in them. The first having d = 4 and the second having d = 7.

The second and third have a common ratio instead and are geometric sequences. The second has r = 2, and the third having r = (-3)

7 0
3 years ago
A closed box has a square base with side length feet and height feet given that the volume of the box is 34 ft.³ express the sur
Deffense [45]

Answer:

\dfrac{2s^3+136}{s}

Step-by-step explanation:

Let the side length of the square base =s feet

Let the height of the box = h

Given that the volume of the box = 34$ ft^3

Volume of the box =s^2h

Then:

s^2h=34$ ft^3\\$Divide both sides by s^2\\h=\dfrac{34}{s^2}

Surface Area of a Rectangular Prism =2(lb+bh+lh)

Since we have a square base, l=b=s feet

Therefore:

Surface Area of our closed box= 2(s^2+sh+sh)

S$urface Area= 2s^2+4sh\\Recall: h=\dfrac{34}{s^2}\\$Surface Area= 2s^2+4s\left(\dfrac{34}{s^2}\right)\\=2s^2+\dfrac{136}{s}\\$Surface Area in terms of length only=\dfrac{2s^3+136}{s}

7 0
2 years ago
Rewrite the following expression using the properties of logarithms: log2z + 2log2z + 4log9y + 12log9x - 2log2y
Mashcka [7]

The rewritten form of the expression given in the task content in which case, the properties of the logarithm are used is; log2(z³/y²) + log9(y⁴x¹²).

<h3>What is the equivalent expression to the logarithmic expression given in the task content?</h3>

It follows from the task content that the logarithmic expression given in the task content is;

log2z + 2log2z + 4log9y + 12log9x - 2log2y

In which case, all terms are to their respective logarithmic bases.

Hence, it follows that; we have;

log2z³ - log2y² + log9y⁴ + log9x¹²

= log2(z³/y²) + log9(y⁴x¹²)

Read more on logarithm laws;

brainly.com/question/10208274

#SPJ1

4 0
2 years ago
Given the linear equation 3x + y = 5, find the slope of its graph
umka2103 [35]

Answer:

B) -3

Step-by-step explanation:

1. First you have to write the equation in slope intercept form. To do that, you must have y be alone on one side.

2. move the 3x to the right side with the 5 by subtracting 3x from both sides. Since 3x will cancel on the left, y will be left alone. y=-3x+5

3. Now that you're in slope intercept form, you can find the slope easily. The slope will always be the number in front of x. In this case, the number in front of x is -3. Therefore, -3 is your slope!

7 0
3 years ago
Read 2 more answers
Other questions:
  • Graph Red beads cost $1 an ounce and gold beads cost $3 an ounce. Juanita wants to purchase a 12-ounce mixture of red and gold b
    10·2 answers
  • 12 laps in 8 minutes or 16 laps in 10 minutes? Which is the greater.
    6·2 answers
  • Jose invested $5000 into a fund with an interest rate of 4.8%.
    10·2 answers
  • I need help with math can someone please help me
    11·1 answer
  • I'm getting two different answers while I'm helping my lil sister out, could anybody help? It's
    10·1 answer
  • Find the domain of the function. (Enter your answer using interval notation.)
    15·1 answer
  • A study reports the mean change in HDL (high-density lipoprotein, or "good" cholesterol) of adults eating raw garlic six days a
    12·1 answer
  • Tevin bought a box of 25 washers for $3.25. How much did Tevin pay per washer?
    6·1 answer
  • Send cute dog pics pls
    10·2 answers
  • How will the graph of line y = -5x + 7 be affected if the 7 is changed to –7?
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!