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
Over [174]
3 years ago
5

Graph y = -­4x2 ­- 2 and its inverse.

Mathematics
1 answer:
CaHeK987 [17]3 years ago
5 0

Be careful with finding its inverse! An inverse only exists for one-to-one functions so we need to restrict the domain such that the quadratic is one-to-one. For brevity, we'll take the domain: x \geq 0 but you could just as easily take x \leq 0.

Being that the quadratic is now one-to-one, we'll try to find its inverse.

By definition, an inverse function is the function flipped across the line y = x. So being that, we need to interchange the x and y coordinates around and then solve for y.

This gives us:

x = -4y^2 - 2 \\ x + 2 = -4y^2 \\ -\frac{1}{4}\left(x + 2\right) = y^2 \\ y = \sqrt{-\frac{1}{4}\left(x + 2\right)}

Now, this function is defined for when y \geq 0 and x \leq -2.

So I'll end with this, what is the relationship between the domain/range of the original function and the domain/range of the inverse?

You might be interested in
Kayla got 18 out of 20 questions correct on a science test what percentage of the questions did kayla get correct
Ksju [112]

18/20=0.9

Move decimal two spaces to the right and include percent sign

90%

7 0
3 years ago
Read 2 more answers
What is the trigonometric ratio for cos C?
Solnce55 [7]
You remember from SOH CAH TOA that
.. Cos = Adjacent/Hypotenuse
.. cos(C) = 80/82 = 40/41 . . . . . . . . . . . seems to match the last selection
8 0
3 years ago
What is the definition for a line segment
Monica [59]

Answer: A line segment is a part of a line. It has 2 endpoints.

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Let A = {1, 2, 3, 4, 5} and B = {2, 4}. What is A ∩ B?
Harlamova29_29 [7]

A\cap B=\{x:x\in A \wedge x\in B\}

A\cap B=\{2,4\}

3 0
3 years ago
Read 2 more answers
Yumi and Juan pick up litter along the highway at the same rate. Yumi picks up litter for 3 miles and takes two hours longer tha
Harlamova29_29 [7]

3/(x+2) = 2/x

multiply both fractions by x(x+2) to cancel out the bottoms

so it becomes 3x = 2x+4

ow subtract 2X from both sides and you get

x = 4

so it took Juan 4 hours

 it took Yumi 2 hours more so 4+2 = 6 hours

7 0
3 years ago
Read 2 more answers
Other questions:
  • Please help me with this problem
    12·2 answers
  • A triangle has two sides of lengths 8and 10 what value could the length of the third side be
    5·1 answer
  • Find the inverse function of f(x)= square root of 2x+2
    8·1 answer
  • What is (5x + 6) - (-x +6)
    9·1 answer
  • Find the vertex for the function<br> <img src="https://tex.z-dn.net/?f=g%28x%29%3D2x%5E%7B2%7D%20%2B12-16" id="TexFormula1" titl
    14·1 answer
  • A stray dog ate 6 of your muffins. That was four thirds of all of them. With how many did you you start?
    7·1 answer
  • Make a table for a function whose graph has a y-intercept of 4 and slope of 2
    9·1 answer
  • Help please Brainiest to whoever is correct
    8·2 answers
  • Solve the quadratic by taking the square root
    5·1 answer
  • Which of the following graphs represent a function? Graph A Graph B Graph Graphc Graph A and Graph C.​
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!