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
Lesechka [4]
3 years ago
8

Find the inverse function of f(x)= square root of 2x+2

Mathematics
1 answer:
Alik [6]3 years ago
6 0

The inverse function of the above function is f(x) = \frac{x^{2} - 2}{2}

You can find the inverse of any function by switching the f(x) and x terms. Once you have done that, solve for the new f(x). Finally, what you'll have remaining is the inverse function. The work is done for you below:

f(x) = \sqrt{2x + 2} ----> Switch the x and f(x)

x = \sqrt{2f(x) + 2} ---> square both sides

x^{2} = 2f(x) + 2 ---> subtract 2 from both sides

x^{2} - 2 = 2f(x) ----> divide both sides by 2

\frac{x^{2} - 2}{2} = f(x) ----> switch the order for formatting sake.

f(x) = \frac{x^{2} - 2}{2}

You might be interested in
Julie had twins that weighed less than 16 pounds together. If each twin weighed the same amount, which of the following inequali
strojnjashka [21]

Answer:

what are the possible inequalities?

Step-by-step explanation:

5 0
3 years ago
Write the number 3.636408 to the nearest ten-thousandth
Elodia [21]

Answer:3.6364

Step-by-step explanation:

Because the 0 isn’t worth nothing & so the 4 stays the same

3 0
3 years ago
Read 2 more answers
Pls help me solve pls show how you got the answer
Dmitry [639]

Polynomial 1 : x²-x²+4x -2+1 = 4x -1

Polynomial 2 : 3x-x-2x²-2+1 = -2x²+2x-1

Polynomial 3 : 4 -2x+x-x²+x²-x² = -x²-x+4

According to the question,

Polynomial 1+Polynomial2+Polynomial3 + Polynomial4 = 6x

=> 4x -1+ (-2x²+2x-1) +(-x²-x+4) + Polynomial4= 6x

=> -3x²-x+2+Polynomial4= 0

<h2>=> 3x²+x -2= Polynomial4</h2>

OPTION B

6 0
3 years ago
Read 2 more answers
Who does e.d.e.n.u.i.t.y and needs help catching up?/ I'm free to help... only up to 8th grade though...
Mekhanik [1.2K]

Answer:

we might be starting it again soon

Step-by-step explanation:

Im in 7th and I might need help!!

4 0
2 years ago
f(x) = 2<img src="https://tex.z-dn.net/?f=x%5E%7B2%7D" id="TexFormula1" title="x^{2}" alt="x^{2}" align="absmiddle" class="latex
loris [4]

Answer:

No answer is possible

Step-by-step explanation:

First, we can identify what the parabola looks like.

A parabola of form ax²+bx+c opens upward if a > 0 and downward if a < 0. The a is what the x² is multiplied by, and in this case, it is positive 2. Therefore, this parabola opens upward.

Next, the vertex of a parabola is equal to -b/(2a). Here, b (what x is multiplied by) is 1 and a =2, so -b/(2a) = -1/4 = -0.25.

This means that the parabola opens upward, and is going down until it reaches the vertex of x=-0.25 and up after that point. Graphing the function confirms this.

Given these, we can then solve for when the endpoints of the interval are reached and go from there.

The first endpoint in -2 ≤ f(x) ≤ 16 is f(x) = 2. Therefore, we can solve for f(x)=-2 by saying

2x²+x-4 = -2

add 2 to both sides to put everything on one side into a quadratic formula

2x²+x-2 = 0

To factor this, we first can identify, in ax²+bx+c, that a=2, b=1, and c=-2. We must find two values that add up to b=1 and multiply to c*a = -2  * 2 = -4. As (2,-2), (4,-1), and (-1,4) are the only integer values that multiply to -4, this will not work. We must apply the quadratic formula, so

x= (-b ± √(b²-4ac))/(2a)

x = (-1 ± √(1-(-4*2*2)))/(2*2)

= (-1 ± √(1+16))/4

= (-1 ± √17) / 4

when f(x) = -2

Next, we can solve for when f(x) = 16

2x²+x-4 = 16

subtract 16 from both sides to make this a quadratic equation

2x²+x-20 = 0

To factor, we must find two values that multiply to -40 and add up to 1. Nothing seems to work here in terms of whole numbers, so we can apply the quadratic formula, so

x = (-1 ± √(1-(-20*2*4)))/(2*2)

= (-1 ± √(1+160))/4

= (-1 ± √161)/4

Our two values of f(x) = -2 are (-1 ± √17) / 4 and our two values of f(x) = 16 are (-1 ± √161)/4 . Our vertex is at x=-0.25, so all values less than that are going down and all values greater than that are going up. We can notice that

(-1 - √17)/4 ≈ -1.3 and (-1-√161)/4 ≈ -3.4 are less than that value, while (-1+√17)/4 ≈ 0.8 and (-1+√161)/4 ≈ 2.9 are greater than that value. This means that when −2 ≤ f(x) ≤ 16 , we have two ranges -- from -3.4 to -1.3 and from 0.8 to 2.9 . Between -1.3 and 0.8, the function goes down then up, with all values less than f(x)=-2. Below -3.4 and above 2.9, all values are greater than f(x) = 16. One thing we can notice is that both ranges have a difference of approximately 2.1 between its high and low x values. The question asks for a value of a where a ≤ x ≤ a+3. As the difference between the high and low values are only 2.1, it would be impossible to have a range of greater than that.

7 0
2 years ago
Other questions:
  • Lamar puts 3 cantaloupes that each weigh 2 pounds onto a scale. He adds 3 bunches of bananas that each have the same weight to t
    5·2 answers
  • Solve.
    5·1 answer
  • the function f(x)=1/6{2/5}x is reflected across the y axis to create the function g(x). which ordered pair is on g(x)
    15·2 answers
  • What property was applied to solve the equation below? I really need help. Picture included.
    10·1 answer
  • Plzzzzzzzz help right answer gets brainly
    15·2 answers
  • What’s the standard form of the line that passes through (7,-3) and has a y-intercept of 2?
    6·2 answers
  • Stu hiked a trail at an average rate of 3 miles per hour. He ran back on the same trail at an average rate of 5 miles per hour.
    6·1 answer
  • The diagram below shows the side view of a ramp used to help load and unload a moving van. Which measurement is closest to the l
    8·1 answer
  • If i pour 1/4 gallon of tea in each of the 4 pitchers. how many gallon in each pitcher
    13·1 answer
  • These two lines are parallel. Write an equation for each.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!