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
olga55 [171]
2 years ago
8

Find an equation for the inverse for each of the following.

Mathematics
1 answer:
IgorLugansk [536]2 years ago
4 0

Answer:

  • <em>To solve these first swap x and y, solve for y and name it inverse function</em>

3. <u>y = -8x + 2</u>

  • x = -8y + 2
  • 8y = -x + 2
  • y = -x/8 + 2/8
  • y = -(18)x + 1/4

f⁻¹(x) = -(18)x + 1/4

-----------------------------------------

4.<u> y = (2/3)x - 5</u>

  • x = (2/3)y - 5
  • (2/3)y = x + 5
  • y = (3/2)x + (3/2)5
  • y = 1.5x + 7.5

f⁻¹(x) = 1.5x + 7.5

-----------------------------------------

5. <u>f(x) = 2x² - 6</u>

  • x = 2y² - 6
  • 2y² = x + 6
  • y² = 1/2x + 3
  • y = \sqrt{1/2x + 3}

f⁻¹(x) = \sqrt{1/2x + 3}

-----------------------------------------

6. <u>y = (x - 3)²</u>

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

f⁻¹(x) = 3 +  \sqrt{x}

You might be interested in
Someone help me out please
uysha [10]

1 step (B): raise both sides of the equation to the power of 2.

(\sqrt{x+3}-\sqrt{2x-1})^2=(-2)^2,\\   (x+3)-2\sqrt{x+3}\cdot \sqrt{2x-1}+(2x-1)=4,\\ 3x+2-2\sqrt{x+3}\cdot \sqrt{2x-1}=4.

2 step (A): simplify to obtain the final radical term on one side of the equation.

-2\sqrt{x+3}\cdot \sqrt{2x-1}=4-3x-2,\\ -2\sqrt{x+3}\cdot \sqrt{2x-1}=2-3x,\\ 2\sqrt{x+3}\cdot \sqrt{2x-1}=3x-2.

3 step (F): raise both sides of the equation to the power of 2 again.

(2\sqrt{x+3}\cdot \sqrt{2x-1})^2=(3x-2)^2,\\ 4(x+3)(2x-1)=(3x-2)^2.

4 step (E): simplify to get a quadratic equation.

4(2x^2-x+6x-3)=(3x)^2-2\cdot 3x\cdot 2+2^2,\\ 8x^2+20x-12=9x^2-12x+4,\\ x^2-32x+16=0.

5 step (D): use the quadratic formula to find the values of x.

D=(-32)^2-4\cdot 16=1024-64=960, \\ \sqrt{D} =8\sqrt{5} ,\\ x_{1,2}=\dfrac{32\pm 8\sqrt{5}}{2} =16\pm 4\sqrt{5}.

6 step (C): apply the zero product rule.

x^2-32x+16=(x-16-4\sqrt{5}) (x-16+4\sqrt{5}) ,\\ (x-16-4\sqrt{5}) (x-16+4\sqrt{5}) =0,\\ x_1=16+4\sqrt{5} ,x_2=16-4\sqrt{5}.

Additional 7 step: check these solutions, substituting into the initial equation.

3 0
3 years ago
A family needs to cross a river in a small raft.
serg [7]

Answer:

so basically you can take more than one trip you can take the mother and the bag at the same time

Step-by-step explanation:

and then you can get the daughter in the son at the same time and then for the final trip you take the father by himself

8 0
2 years ago
Help asap !! will get branliest.​
kompoz [17]

Answer:

0.8

Step-by-step explanation:

(2 x 10^-4)

= 0.0002

(4x10^3)

= 4000

0.0002 x 4000 = 0.8

7 0
3 years ago
A college statistics class at a nearby university has 1,000 students enrolled in it. On a recent exam, the mean score was 75% wi
IceJOKER [234]

Answer:

38.11%

Step-by-step explanation:

Given that:

Mean (μ) = 75, standard deviation (σ) = 5

Z score is a measure in statistics to determine the variation of a raw score from the mean. It is given by the equation:

z=\frac{x-\mu}{\sigma}

To calculate the percentage of students scored between a 73 and 78 (C grade), we need to find the z score for 73 and then for 78.

For x = 73, the z score is:

z=\frac{x-\mu}{\sigma}=\frac{73-75}{5} =-0.4

For x = 78, the z score is:

z=\frac{x-\mu}{\sigma}=\frac{78-75}{5} =0.6

From the probability distribution table:

P(73 < x < 78) = P(-0.4 < z < 0.6) = P(z < 0.6) - P(z < -0.4) = 0.7257 - 0.3446 = 0.3811 = 38.11%

4 0
3 years ago
#54 Simplify and write the answers using positive exponents only.
kramer
Gg easy

remember
(x^m)/(x^n)=x^(m-n)
and
(x^m)^n=x^(mn)
and
(xyz)^m=(x^m)(y^m)(z^m)
and
(m/n)^a=(m^a)/(n^a)
and
x^-n=1/(x^n)

so
( \frac{6mn^{-2}}{3m^{-1}n^2} )^{-3}=
( \frac{6}{3} )^{-3}( \frac{m}{m^{-1}} )^{-3}( \frac{n^{-2}}{n^2} )^{-3}=
(2^{-3})((m^2)^{-3})((n^{-4})^{-3})=
( \frac{1}{2^3})(m^{-6})(n^{12})=
( \frac{1}{8} )( \frac{1}{m^6})(n^{12})=
\frac{n^{12}}{8m^6}

8 0
3 years ago
Other questions:
  • Nicky is considering two different companies for textbook rentals. For
    5·1 answer
  • Sovle for x in the equation x2+14+17 =-96
    12·2 answers
  • Please help me! :) I will give 15 thank yous! Please help<br> 
    5·1 answer
  • If the midpoint of segment AB is M(1,-3) and B(5,-10), find the coordinates of point A.
    15·1 answer
  • Plzz help and show work plzz
    15·1 answer
  • A survey was conducted of students at a high school and at a college to determine students favorite subjects the result are show
    6·1 answer
  • ME LO RESUELVEN PORFAA
    13·1 answer
  • Both questions I need help with please!!
    14·2 answers
  • Write two numbers that multiply to the value on top and add to the value on bottom.<br> 42<br> 13
    8·1 answer
  • What is the value of this expression?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!