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
Determine the slope of (5,6) &amp; (3,9)???​
Nadusha1986 [10]

Answer:

3/-2

Step-by-step explanation:

3 0
3 years ago
the ratio of cars to trucks on the parking lot is 2:3 there are 24 trucks on the lot what is the total number of vehicles on the
SVEN [57.7K]

x=16

Explanation

the ratio is 2:3

it means for every 2 cars, there are 3 trucks

Now, it the total of trucks is 24,the proportion must be the same, so

Step 1

Let

x represents the number of cars for 24 trucks

\frac{\text{2 cars}}{3\text{ trucks}}=\frac{x}{24\text{ trucks}}

Step 2

solve for x

\begin{gathered} \frac{\text{2 cars}}{3\text{ trucks}}=\frac{x}{24\text{ trucks}} \\ 2\cdot24=3\cdot x \\ x=\frac{2\cdot24}{3} \\ x=\frac{48}{3} \\ x=16 \end{gathered}

Hence, the answer is 16

4 0
1 year ago
Tentukan panjang BC dari gambar berikut​
EleoNora [17]

Answer:

man I

Step-by-step explanation:

hey

8 0
3 years ago
Read 2 more answers
Help pls im trying to figure out my money i'm saving for a phone ill give brainliest if u can help. i have $16 rn and on march 1
Anni [7]

Answer:

58 weeks.

Step-by-step explanation:

so 303 - 16 you would have 287$ left to earn, then your going to divide it by 5.

it will take you 58 weeks to get to 303$

7 0
2 years ago
Read 2 more answers
△BCD ​ is a right triangle. The length of the hypotenuse is 18 centimeters. The length of one of the legs is 14 centimeters. Wha
Romashka-Z-Leto [24]

Answer:

The answer to your question is   b = 11.31 cm  or   8\sqrt{2} cm

Step-by-step explanation:

Data

hypotenuse = 18 cm

one leg = 14 cm

second leg = ?

Process

1.- Use the Pythagorean Theorem to solve this problem

                 c² = a² + b²

c = hypotenuse

a = longer leg

b= shorter leg

2.- Substitution

                        18² = 14² + b²

-Solve for b

                         b² = 18² - 14²

-Simplify

                         b² = 324 - 196

                         b² = 128

-Find the prime factors of 128

                          128   2

                            64  2

                             32  2

                             16  2

                              8  2

                              4  2

                              2  2

                               1

          128 = 2⁶2¹                                    

-Result

                         b = 11.31   or   8\sqrt{2}

5 0
2 years ago
Other questions:
  • Identify the slope of the line shown in the graph below: Graph of a vertical line with an x intercept of 5.
    5·2 answers
  • What is the simplified form of 144x^36?<br> O 12x6<br> O 12x18<br> O 72x6<br> 072x18
    15·1 answer
  • What is the answer for 12 over 75 (fraction)
    7·1 answer
  • Can someone help and tell me how to do this
    7·1 answer
  • What is 342.5752 divided by 4
    5·2 answers
  • I need help with graphing
    14·1 answer
  • Use the parallelogram below to solve for x x , then find the length of all 4 sides. figure
    9·1 answer
  • Divide. Give the quotient and remainder.<br> 33 - 8<br> :))))
    8·2 answers
  • How can I make an equation that equals 74 with using the digits/numbers 1 2 3 4 and 0 once and only once in the equation. Every
    5·2 answers
  • Please help me I need help with solving this equation worth 30 points
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!