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
kramer
3 years ago
13

25 POINTS AND BRAINLIEST FOR THESE!

Mathematics
2 answers:
Verizon [17]3 years ago
8 0

Answer:

Step-by-step explanation:

Hello,

For any function f which has an inverse function we can write

x=(f^{-1}of)(x)=(fof^{-1})(x)=f(f^{-1}(x))

This is why, in practice, to find the inverse of f we will consider f(x) = y and we will look for x as a function of y, so we switch x and y and solve for y. Let's do it.

<u>Step 1 - The function f(x) can be written as a variable.  </u>\boxed{y}=f(x)<u />

f(x) = y = 5x + 2

<u />

<u>Step 2 - switch the variables x <-> y</u>

x = 5y + 2

subtract 2 to both parts of the equation

<=> x - 2 =  5y + 2 - 2 = 5y

divide by 5 both parts of the equation

y=\dfrac{x-2}{5}

It means that the inverse of f is as below.

\boxed{ \ f^{-1}(x)=\dfrac{x-2}{5}\ }

<u>Step 3 - Find the inverse of g(x)</u>

We already found that the inverse of f is g, so the inverse of g is f.

Let's do it again.

g(x)=y=\dfrac{x-2}{5} \ \ \text{ switch x and y } \\ \\ x= \dfrac{y-2}{5} \ \ \text{ solve for y }\\ \\ y-2=5x \ \ \text{ mulitply by 5 both parts of the equation } \\ \\ y = 5x+2 \ \ \text{ add 2 to both parts of the equation }

And we found what we already known, meaning f is the inverse of g.

(gof)(x)=(fog)(x)=x

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

padilas [110]3 years ago
4 0

Answers and Step-by-step explanation:

<u>Step 1</u>:

We want to find the variable that ff(x) represents. Well, we know it can't be x because we already have x on the other side of the equation: ff(x) = 5x + 2.

So, ff(x) must equal y.

Since ff(x) = y, we know then that ff(x) = y = 5x + 2. And our equation is:

y = 5x + 2

<u>Step 2</u>:

Let's switch the variables now. This means that what used to be y will be x and what used to be x will be y:

y = 5x + 2  ⇒  x = 5y + 2

Subtract 2 from both sides:

5y = x - 2

Divide by 5 from both sides:

y = (x - 2)/5

<u>Step 3</u>:

Let's find the inverse of g(x) by doing the exact same thing as we did with ff(x):

g(x) = y = (x - 2)/5

Switch the variables:

y = (x - 2)/5  ⇒      x = (y - 2)/5

Multiply by 5 on both sides:

5x = y - 2

Add 2 to both sides:

y = 5x + 2

Notice that this is the exact same as ff(x)! This means that ff(x) and g(x) are inverses.

You might be interested in
Help ASAP!!!!!!!!!..........
Semenov [28]

Answer:

14x

Step-by-step explanation:

please mark this answer as the brainlest

6 0
3 years ago
Read 2 more answers
Gary has 2 red apples, 2 green apples, and 2 yellow apples in a sack. He also has 2 packages of peanuts, 2 packages of almonds,
o-na [289]
1/3 or approximately 0.3333333334 percent
3 0
3 years ago
For the triangles to be congruent by HL, what must be the value of x?
umka21 [38]

Answer:

4!

Step-by-step explanation:

The answer is not 8, its 4. Just took the test!

8 0
3 years ago
Read 2 more answers
The graph below shows the distance, y, in miles, of a bird from its nest for a certain amount of time, x, in minutes: Graph titl
Degger [83]

<u><em>Answer:</em></u>

The initial value is 3

It represents the distance between the bird and its nest before any elapsed time which is 3 miles.

<u><em>Step-by-step explanation:</em></u>

The graph is shown in the attached image.

<u>The general form of a straight line is:</u>

y = mx + c

where:

m is the slope and c is the y-intercept.

The y-intercept is also known as the initial value. It is the value of y at x=0.

From the givens, we can note that at x = 0, the y-value is 3. This means that the y-intercept is 3.

Now, in the problem, x represents the time in minutes while y represents the distance of the bird from the nest in miles.

At x = 0, meaning before any time elapsed, the distance of the bird from its nest was 3 miles.

Hope this helps :)

4 0
3 years ago
Read 2 more answers
6. Marisol plans to make 9 mini-sandwiches for
Oksanka [162]

Answer:

18/4

Step-by-step explanation: in order to get an equivalent ration just multiply both numerator and denominator by the same number

in this case I multiplied by 2 and got 18/4

3 0
3 years ago
Read 2 more answers
Other questions:
  • What is the value of 2x3squared +x2squared when x = 3
    13·1 answer
  • Given the points (-1,-5) and D(-7, 11). find the coordinates of point E
    12·1 answer
  • How can this be solved? (With explanation please.) Sorry about the writing and marks.
    7·1 answer
  • the sum of present ages of a father and his son is 60 years. if both of them live until the son becomes as well as the father is
    14·1 answer
  • What is 0.95 in a fraction and percentage??
    12·2 answers
  • X + 8 = -15<br> What does x= ???
    10·1 answer
  • Other than squares, the polygons that can be the faces of a Platonic solid are
    6·1 answer
  • Suponga que el monto promedio de compras por cliente de una empresa es de $128.45 y una desviación de $18.26
    15·1 answer
  • HELP With this question
    7·1 answer
  • The length of a rectangular garden is 30 yards more than the width. The perimeter is 300 yards. Find the length and width
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!