What is an example of an inverse function?

Answers

Answer 1

Suppose that f and g are inverse functions, with f(g(x)) = g(f(x)) = x. A function's inverse retrieves the initial value, and g(y) = (y-5)/2 = x is the inverse of f. (x).

What is a inverse function theorem?

The inverse function theorem in mathematics provides a necessary requirement for a function to be invertible in the vicinity of a point in its domain, meaning that its derivative is continuous and non-zero at the point. This condition is relevant to differential calculus.

The derivative of the inverse function is also given a formula by the theorem. This theorem in multivariable calculus can be extended to any continuously differentiable, vector-valued function whose Jacobian determinant is nonzero at a point in its domain, providing a formula for the Jacobian matrix of the inverse.

The inverse function theorem also applies to complex holomorphic functions, differentiable functions between Banach spaces, differentiable functions between manifolds, and so forth.

Picard and Goursat used an algebraic approach to prove the theorem in the beginning.

Hence, Suppose that f and g are inverse functions, with f(g(x)) = g(f(x)) = x. A function's inverse retrieves the initial value, and g(y) = (y-5)/2 = x is the inverse of f. (x).

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Related Questions

what is the mass of 20 buckets

Answers

20xmass of one bucket
10 percent is the mass number

What is the area of the parallelogram?
3
2

Answers

Answer: 6

Answer Explanation: Area=Base*Height

Find the second base of a trapezoid with an area of 96 inches, a height of 8 inches, and a 1st base measuring 11 inches.

Answers

Answer:

13

Step-by-step explanation:

11+x=y

yx8=z

z/2=96

96x2=192

192/8=24

24-11=13

x=13

Please answer correctly!! I’ll mark as brainliest!

No links no fake answers

Answers

#5 is 21 but I don’t know about the first one

Answer:

The first answer is 31.5.

The second is 21.

Step-by-step explanation:

What are the domain and
range
of an exponential parent function?
A. The domain is positive real numbers (x > 0), and the range is all
real numbers.
B. The domain is all real numbers, and the range is nonnegative real
numbers (y≥ 0).
C. The domain is nonnegative real numbers (x≥ 0), and the range is
all real numbers.
D. The domain is all real numbers, and the range is positive real
numbers (y > 0).

Answers

Answer: it’s D

Step-by-step explanation:

The domain and the range of an exponential parent function mean that the domain is all real numbers and the range signifies positive real numbers y > 0.

What is an exponential parent function?

The simplest parent function of an exponential function takes the form:

[tex]\mathbf{f(x) = p^x}[/tex], where p refers to the base.

So, if we have a number such that x = 3 and the base is 2

f(3) = 2³f(3) = 6

Therefore, we can conclude that the domain of an exponential parent function is all real numbers, and the range is positive real numbers (y > 0).

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Please help me with this problem!!

Answers

Yes, the correct answer would be 45. Good luck

Which of the following could be used to estimate 75 -32?
A. 80 - 30
B. 70 - 30
C. 80-40
D. 70 - 40​

Answers

Answer:

b

Step-by-step explanation:

the answer when not rounded is 43.

A box of chocolates has 5 creme filled, 8 peanut butter filled, and 7 caramel filled chocolates. What is the probability, expressed as a
percent of randomly selecting a creme filled chocolate?
A) 5%
B) 15%
C) 20%
D) 25%

Answers

Answer:

25%

Step-by-step explanation:

Step 1: Add all the possible choices up

8 + 5 + 7 = 20

Step 2: Note that your finding the probability for creme filled ones

Step 3: Make it a fraction

5 creme filles ones out of 20

5/20

Step 4: Simplify

1/4

Step 5: Convert into a decimal (if you don't already know it)

1 ÷ 4 =

.25

Step 6: Multiply by 100 to find percentage

.25 × 100 = 25%

please help me if you do not know do not answerr​

Answers

Answer:

Quadratic

Step-by-step explanation:

Example of linear is 2x + 3

Example of quadratic is x² + 2x + 3

Example of cubic is x³ + 2x² + 3x + 4

Example of quartic is x⁴ + 2x³ + 3x² + 4x + 5

Finde
3 rational number
7 and 8

Answers

Answer:

7/1; 4/2=2;8/1

7 is rational number because 7/1 = 7

8 = 4 x 2 = 4/1 x 2/1 and both rational.

Step-by-step explanation:

Multiply by any number/ same with both

7/1×6=42/6

8/1×6=48/6

So,

43/6,44/6,45/6 Answer

hope it helps

A parabola has a vertex (-3, -2) and contains the point (-5, 6). Write the equation for this parabola in vertex form.

Answers

Answer:

[tex]y = 2(x +3)^2 -2[/tex]

Step-by-step explanation:

Given

[tex](h,k) = (-3,-2)[/tex] --- vertex

[tex](x,y) = (-5,6)[/tex] --- point

Required

Determine the equation

The general form is:

[tex]y = a(x - h)^2 + k[/tex]

First, we solve for a:

Substitute [tex](h,k) = (-3,-2)[/tex] and [tex](x,y) = (-5,6)[/tex] in [tex]y = a(x - h)^2 + k[/tex]

[tex]6 = a(-5 - (-3))^2 - 2[/tex]

[tex]6 = a(-2)^2 - 2[/tex]

[tex]6 = 4a - 2[/tex]

Solve for a

[tex]4a = 6 + 2[/tex]

[tex]4a = 8[/tex]

[tex]a = 2[/tex]

So:

[tex]y = a(x - h)^2 + k[/tex]

[tex]y = 2(x - (-3))^2 -2[/tex]

[tex]y = 2(x +3)^2 -2[/tex]

UNIT TEST:
TVAH: GeometryB Unit 4 Test
The perimeter of the base of a right square pyramid is 32 cm. The height of the
pyramid is 8 cm.
What is the volume of the pyramid?
O 256 cm
O 170.67 cm
o 85.33 cm
O 512 cm
2 3
4
5
6
7
Next
8 9 10 11
o
9

Answers

Answer:

170.67 cm^3

Step-by-step explanation:

The volume is given by ...

 V = 1/3s²h

We are given that 4s=32, so s=8. We are also given that h=8. (All linear dimensions are in centimeters.) Then the volume is ...

 V = (1/3)(8²)(8) = 512/3 = 170.67 . . . . cm³

Answer:

170.67 cm^3

Step-by-step explanation:

took the test

Use the graph of the function f(x) = (x + 1)² + 2. Identify the vertex and
the axis of symmetry.

Answers

1. Vertex: f(x)=x^2+2x+3
=> a=1 b=2
=> x=-2/2*1 => x=-2/2
=> x=-1
=> (-1,2)

2. Axis of symmetry: x=-1

help fast pls .. Find the equation for g(x) by substituting the known point (1, 4) and solving for k.

Answers

Answer:

6=k×2

k=3

g(x)=k f(x)

g(x)=3 |x|

Which of these does NOT represent the distance a car travels when going 55 miles per hour?

Answers

Answer:

the first one

Step-by-step explanation:

just trust me

The probability that is will rain today is 65%, and the probability that it will rain tomorrow is 25%.

The probability that it will rain both days is 35%.

What is the probability that is will rain today or tomorrow?

Answers

Answer:

65%

Step-by-step explanation:

Help ASAP, ACD and DCB form a linear pair

Answers

Answer:

40

Step-by-step explanation:

because 180- 140 = 40

a linear pair means they equal 180

The measure of angle ACD (∠ACD) is 40 degrees.

Given that angles ACD and DCB forms a linear pair, also m ∠DCB = 140°,

We are asked to find the measure of ∠ACD,

So,

If angles ACD and DCB form a linear pair, it means that their sum is equal to 180 degrees.

Let's denote the measure of angle ACD as x.

So, we have the equation:

m∠ACD + m∠DCB = 180°

Substituting the given value for m∠DCB:

x + 140° = 180°

To solve for x, we can subtract 140° from both sides of the equation:

x = 180° - 140°

x = 40°

Therefore, the measure of angle ACD (∠ACD) is 40 degrees.

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HELP PLEASE: without doing the math, determine which is greater, 50 times 1/5 or 50 divided by 1/5. explain your reasoning.

Answers

Answer:

The first option

Step-by-step explanation:

Have a nice day :)

Gllberto invests $10,000 in a savings account that pays 4.75% simple interest. If Gilberto
makes no withdrawals or deposits to the account, how much will be in the account after 7
years?

Answers

Answer:

$13,325

Step-by-step explanation:

Hey! Please answer this fast, it’s due soon. It’s fractions

Answers

Answer:

3/12 - 8/12= 5/12

10/12 - 5/12= 5/12

Find the value of x, y, and z.
Round to the nearest tenth if needed.
Please help me

Answers

Answer:

x = 26.5

y = 12.0

z = 13.4

Step-by-step explanation:

✔️To find x, apply the leg rule, which is:

Hypotenuse/leg = leg/part

Hypotenuse = 30

Leg = x

Part = 30 - 6 = 24

Plug in the values into the equation

30/x = x/24

Cross multiply

x² = 30*24

x² = 720

x = √720

x = 26.5 (nearest tenth)

✔️Apply the triangle altitude theorem to find y:

Based on the theorem, h = √(ab)

Where,

a = 6

b = 30 - 6 = 24

h = y

Plug in the values

y = √(6*24)

y = √144

y = 12

✔️Apply the leg rule, Hypotenuse/leg = leg/part to find z:

Hypotenuse = 30

Leg = z

Part = 6

Plug in the values into the equation

30/z = z/6

Cross multiply

z² = 30*6

z² = 180

z = √180

z = 13.4 (nearest tenth)

Amanda, Boris, and Jose sent a total of 124 text messages during the weekend. Amanda sent 8 fewer messages than Jose
Boris sent 4 times as many messages as Jose. How many messages did they each send?

Answers

Answer:

Amanda= 14

Boris = 88

Jose= 22

Step-by-step explanation:

Amanda= jose-8

Boris = 4×jose

Jose= Jose

total all = 124

(jose-8)+(jose×4)+(jose)= 124

so we substitute jose with X .

(X-8)+(4X)+(X)=124

6X-8= 124.

6X=124+8

X=132/6

X= 22.

so that total jose is 22, minus 8 we get Amanda, times 4 we get Boris.

6. Rewrite each of the following expressions without roots by using fractional exponents.

Please help! I have tried to look it up everywhere and I don’t understand how to do it. Anything helps!!

Answers

Answer:

A. x¹/²

B. x¹/³

C. x¹/⁷

D. x⁵/²

E. x¹¹/³

F. 1 / x¹/⁴

G. 1 / x²/³

H. 1 / x⁹/²

Step-by-step explanation:

A. √x

Recall

√M = M¹/²

Therefore,

√x = x¹/²

B. ³√x

Recall

ⁿ√M = M¹/ⁿ

Therefore,

³√x = x¹/³

C. ⁷√x

Recall

ⁿ√M = M¹/ⁿ

Therefore,

⁷√x = x¹/⁷

D. √x⁵

Recall

√Mⁿ = Mⁿ/²

Therefore,

√x⁵ = x⁵/²

E. ³√x¹¹

Recall

ⁿ√Mᵃ = Mᵃ/ⁿ

Therefore,

³√x¹¹ = x¹¹/³

F. 1 / ⁴√x

Recall

ⁿ√M = M¹/ⁿ

Therefore,

1 / ⁴√x = 1 / x¹/⁴

G. 1 / ³√x²

Recall

ⁿ√Mᵃ = Mᵃ/ⁿ

Therefore,

1 / ³√x² = 1 / x²/³

H. 1 / √x⁹

Recall

√Mⁿ = Mⁿ/²

Therefore,

1 / √x⁹ = 1 / x⁹/²

Which choice shows three lengths that cannot be the lengths of the three sides of a triangle? 2 cm, 8 cm, 8 cm B. 2 cm, 3 cm, 6cm C. 4cm, 5 cm, 7 cm . D. S cm. 6 cm. 9 cm​

Answers

Answer:

A

Step-by-step explanation:

Because the lengths are way off for A.

2cm, 8cm, 8cm

Find the area and perimeter of the shaded regions below. Give your answer as a completely simplified exact value in terms of pi (no approximations). The figures below are based on semicircles or quarter circles.

*I found the area but I can't seem to find the perimeter

Answers

Answer:

[tex] A=(8 \pi +40) cm^2 [/tex]

[tex] P=(4 \pi + 4\sqrt {29}) \: cm[/tex]

Step-by-step explanation:

For semicircle:

Diameter = 8 cm

Radius (r) = 8/2 = 4 cm

For triangle:

Base (b) = 8 cm

Height (h) = 10 cm

Area of the shaded region

[tex] A=\frac {1}{2} \pi r^2 +\frac {1}{2}b.h[/tex]

[tex] A=\frac {1}{2} \pi (4)^2 +\frac {1}{2}(8).(10)[/tex]

[tex] A=(8 \pi +40) cm^2 [/tex]

By Pythagoras Theorem:

[tex] AC = BC = \sqrt {4^2 +10^2}[/tex]

[tex] AC = BC = \sqrt {16 +100}[/tex]

[tex] AC = BC = \sqrt {116}[/tex]

[tex] AC = BC =2\sqrt {29}[/tex]

[tex] P= \frac {1}{2} \times 2\pi r+ AC + BC[/tex]

[tex] P= \pi (4)+ 2\sqrt {29} + 2\sqrt {29}[/tex]

[tex] P=(4 \pi + 4\sqrt {29}) \: cm[/tex]

Three friends are sharing 4 cups of lemonade. If they share the lemonade equally, how many cups will each friend get?

Answers

Answer:

3/4 of a cup or .75 of a cup

Step-by-step explanation:

1.3 bc you divide 4 by 3

What does x equal to?

Answers

Answer:

x = 25°

Step-by-step explanation:

the angle adjacent to the 130 angle is 50 degrees

x = 180-(105+50)

x = 180-155

x = 25

solving by elimination
2x+8y=6
5x+20y=15

Answers

Answer:

Solve for  x  in the first equation.

Subtract  8 y  from both sides of the equation.

2 x = 6 − 8 y

5 x + 20 y = 15

Divide each term by  2  and simplify.

Divide each term in  

2 x /2 =  6/2  − 8 y/2  

5 x + 20 y = 15

Cancel the common factor of  2 .

Cancel the common factor.

2 x /2  =  6 /2  + (− 8 y)/ 2

Step-by-step explanation:

I don't have room to put the rest. So go to math-way

Number 1 help please

Answers

Answer:

D

Step-by-step explanation:

the figure is in the origin therefore no reflection will affect the shape

If a varies directly with x squared, and a = 8 when x = 4 find the constant variation of k

Answers

Answer:

k = 0.5

Step-by-step explanation:

Given a varies directly with x² then the equation relating them is

a = kx² ( k is the constant of variation )

To find k use the condition a = 8 when x = 4 , then

8 = k × 4² = 16k ( divide both sides by 16 )

0.5 = k

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