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Y_Kistochka [10]
3 years ago
13

If f(x) and g(x) are inverse functions of each other, which of the following statements is true?

Mathematics
1 answer:
Kazeer [188]3 years ago
5 0

The true statement is (g•f)(x) = x ⇒ answer D

Step-by-step explanation:

Let us revise the relation between a function and its inverse

  • The inverse of the function f(x) = y is g(y) = x
  • The function and its inverse are reflections across the line y = x
  • The graph of f(x) and the graph of its inverse g(x) are intersected at a point lie on the line y = x
  • f(g(x)) = g(f(x)) = x

Example:

g(x) is the inverse function of f(x)

∵ f(x) = x - 5

∵ f(x) = y

∴ y = x - 5

To find the inverse switch x and y and find y

∵ x = y - 5

- Add 5 to both sides

∴ x + 5 = y

∴ g(x) = x + 5

Let us find f(g(x)) and g(f(x)0

To find f(g(x)) substitute x in f(x) by g(x)

∵ f(g(x)) = (x + 5) - 5

∴ f(g(x)) = x + 5 - 5

∴ f(g(x)) = x

To find g(f(x)) substitute x in g(x) by f(x)

∵ g(f(x)) = (x - 5) + 5

∴ g(f(x)) = x - 5 + 5

∴ g(f(x)) = x

Now let us solve the question

∵  f(x) and g(x) are inverse functions of each other

∴ f(g(x)) = g(f(x)) = x

The true statement is (g•f)(x) = x

Learn more:

You can learn more about the inverse function in brainly.com/question/2456302

#LearnwithBrainly

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Verdich [7]

Answer:

The surface area of the pyramid is 466,137 squared cubits

Step-by-step explanation:

This is simply asking us to find the surface area of the square based pyramid with the given dimensions.

The first thing we need to know is the principle for finding the surface area of such pyramidal shapes. To get the surface area of a pyramid, we will have to add the base area to the area of the side faces ( lateral area)

The base area of the square based pyramid, will be the same as the area of a square which is = 453 cubits X 453 cubits =205209 cubits^{2}

The lateral area has already been given to us as 260,928 squared cubits.

The surface area of the pyramid is 260,928 + 205209 = 466137 squared cubits

Hence, the surface area of the pyramid is 466137 squared cubits

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3 years ago
Mike travels 13 miles per 2 hours on his bike.
LiRa [457]

Answer:

It took Markus half an hour to drive home from work.  He averaged 34 miles per hour.  How far does Markus live from his work?

Solution

We are given that it takes 1/2 an hour for the trip.  This is a time:

       t  =  1/2

We are given that he averages 34 miles per hour.  This is a rate:

       r  =  34

We are asked how few he has traveled.  This is a distance.  We use the d=rt equation:

       d  =  rt

           =  (34)(1/2)

           =  17

Markus lives 17 miles from work.

Now try one by yourself.  If you want to see the answer, put your mouse on the yellow rectangle and the answer will appear.

Exercise 1

The current along the beach is moving towards the south at 1.5 miles per hour.  If a piece of debris is placed into the water, how far will the current take it in 6 hours?

Step-by-step explanation:

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alina1380 [7]

Answer:

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Step-by-step explanation:

not sure what the wuestion is but using the formula. A^2 + B^2 = C^2 we find that 100 / 4 = 25 and the square root of 25 is 5

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Solve system of equation algebraically <br> y = 2x - 3<br> x + y = 18
natima [27]

Answer:

x = 7

y = 11

Step-by-step explanation:

Given the system;

y = 2x - 3

x + y = 18

1. Approach

The easiest way to solve this system of equations is to solve the second equation for the variable (y). Then add the systems, use algebra to solve for the value of (x), then substitute that value back into one of the original equations to solve for the value of (y). Another name for the method in use is the method of elimination, this is when a [erspm manipulates one of the equations in a system of the equation such that when they add the equations, one of the variables eliminatates. Thus, they can solve for the other variable and the backsolve for the value of the unknown variable.

2. Solve one of the equations for a variable

Manipulate the system such that each equation is solved for the same variable,

x + y = 18

Inverse operations,

x + y = 18

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x + y - 18 = 0

   -y         -y

x - 18 = -y

3. Use elimination

Now substitute this back into the original system,

y = 2x - 3

-y = x - 18

Add the systems,

y = 2x - 3

-y = x - 18

_________

0 = 3x - 21

Inverse operations,

0 = 3x - 21

+21       +21

21 = 3x

/3    /3

7 = x

4. Find the value of the unknown variable

Backsovle to find the value of (y),

x + y = 18

Substitute,

7 + y = 18

Inverse operations,

7 + y = 18

-7        -7

y = 11

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2 years ago
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Answer is 6.88 cm

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radius of circle = 5÷tan(36°) = 6.88 cm

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