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
Lera25 [3.4K]
2 years ago
11

If f(x) and it's inverse function, f^1(x) are both plotted on the same coordinates plane what is their point of intersection

Mathematics
2 answers:
svet-max [94.6K]2 years ago
7 0
The answer is an equation, a condition:

f(x) = f^(-1)(x), then apply f(x) again: f(f(x) ) = f(f^-1(x)) = x,

f(f(x)) =x, that means that:

The point of intersection is the point where applying f(x) twice it results in the identity. A similar argument takes you to f^(-1)(f^(-1)(x)) = x.

Furthermore, the final answer is the point where f(x)=x (which coincides with f^(-1)(x)=x). That is the value of x where the function crosses the line y=x. If there is no such point, then f(x) and f^(-1)(x) will never cross each other.

I can see the proof graphically, so I can't post it.

For a line, it always works:

f(x) = ax+b, f^(-1)(x) = (x-b)/a,   ax+b = (x-b)/a --> a^2x+ab=x-b,

x = -(a+1)*b/(a^2-1) = -b/(a-1). Which is indeed where f(x)=x.
Masja [62]2 years ago
6 0

Answer:

Point of intersection of two graph: It is defined as the point at which where both graph cut to each other.

Step-by-step explanation:

We are given that f(x) and its inverse function is f^{-1{(x) are poltted on the same coordinate plane.

We have to find the point of intersection.

Point of intersection of two graph: It is defined as the point at which where both graph cut to each other and value of both functions are equal at the point.

Suppose a function f(x)=2x+1

f^{-1}(x)=\frac{x-1}{2}

Substitute x=-1 then we get

f(-1)=2(-1)-+1=-1

f^{-1}(-10)=\frac{-1-1}{2}=-1

Therefore, the point of intersection is (-1,-1) because the value of both functions are equal at this point.

You might be interested in
Urgent!! Will mark brainliest!!
horsena [70]

Answer:

1) x is negative and y is positive ⇒ last answer

2) cotФ = -12/35 ⇒ second answer

3) The right identity is cot²Ф - csc²Ф = -1 ⇒ last answer

Step-by-step explanation:

* For any point (x , y) lies on the terminal side of the angle Ф

 in standard position

* x = cosФ and y = sinФ

- If Ф in the first quadrant, then x , y are positive

∴ All trigonometry functions are positive

- If Ф in the second quadrant, then x is negative , y is positive

∴ sinФ only is positive

- If Ф in the third quadrant, then x is negative , y is negative

∴ tanФ only is positive

- If Ф in the fourth quadrant, then x is positive , y is negative

∴ cosФ only is positive

* Lets solve the problems

∵ Ф = 3π/4 ⇒ (135°)

∴ It lies on the second quadrant

∴ x is negative and y is positive

* Lets revise the reciprocal of sinФ, cosФ and tanФ

- cscФ = 1/sinФ

- secФ = 1/cosФ

- cotФ = 1/tanФ

∵ secФ = -37/12

∴ cosФ = -12/37

∵ π/2 < Ф < π

∴ Ф lies on the second quadrant

∴ cotФ is negative values

∵ tan²Ф = sec²Ф - 1

∵ secФ = -37/12

∴ tan²Ф = (-37/12)² - 1 = 1225/144 ⇒ take√ for both sides

∴ tanФ = ± 35/12

∵ cotФ = ± 12/35

∵ cotФ is negative value

∴ cotФ = -12/35

* In the standard position of the angle Ф the terminal

 of it lies on the unit circle O

- By using Pythagorean theorem

∵ x² + y² = 1

∵ x = cosФ and y = sinФ

∴ cos²Ф + sin²Ф = 1 ⇒ (1)

∴ cos²Ф = 1 - sin²Ф

∴ sin²Ф = 1 - cos²Ф

* Divide (1) by cos²Ф

∴ cos²Ф/cos²Ф + sin²Ф/cos²Ф = 1/cos²Ф

* Remember sin²Ф/cos²Ф = tan²Ф and 1/cos²Ф = sec²Ф

∴ 1 + tan²Ф = sec²Ф ⇒ (2) ⇒ subtract 1 from both sides

∴ tan²Ф = sec²Ф - 1 ⇒ subtract sec²Ф from both sides

∴ tan²Ф - sec²Ф = -1

* Divide (1) by sin²Ф

∴ cos²Ф/sin²Ф + sin²Ф/si²Ф = 1/sin²Ф

* Remember cos²Ф/sin²Ф = cot²Ф and 1/sin²Ф = csc²Ф

∴ cot²Ф + 1 = csc²Ф ⇒ (3) ⇒ subtract 1 from both sides

∴ cot²Ф = csc²Ф - 1 ⇒ subtract csc²Ф from both sides

∴ cot²Ф - csc²Ф = -1

* The right identity is cot²Ф - csc²Ф = -1

3 0
3 years ago
The sum of 5 times a number and <br> minus −​2, plus 7 times a​ number
Olenka [21]

Answer:

12x + 2

Step-by-step explanation:

Let the number be represented by x.

Then five times the number = 5*x

Seven times the number = 7*x

Sum of 5 times the number minus -2 = \[5*x - (-2)\] = \[5x +2\]

Adding seven times the number to this expression yields, \[5x+2+7x\]

\[= (5+7)x+2\]

\[= 12x+2\]

So the simplified expression corresponds to 12x + 2.

6 0
3 years ago
Solve the following:<br><br> 1 - .008 =
kykrilka [37]

Answer:

0.992

Step-by-step explanation:

do you not have a calculator

3 0
2 years ago
Read 2 more answers
SOMEONE HELP ASAP I HAVE THREE MINUTES PLEASEEEEEEEEEEEEEEEEEE I'LL GIVE BRAINLIEST TO FIRST REAL ANSWER
Aleksandr [31]
X=1
F(x) = 2
I am pretty sure I hope this helps
4 0
2 years ago
The problem involves a conversion from feet to miles. How many feet are in one mile? Use the Internet or another resource if you
Ghella [55]

The value of the 1 mile is equal to 5280 feet

We have given that,

The problem involves a conversion from feet to miles.

We have to determine how many feet are in one mile.

<h3>What is the conversion form?</h3>

Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.

1 mile is equal to 5280 feet

Therefore we get,

1mile=5280 feet.

To learn more about the conversion visit:

brainly.com/question/23718955

#SPJ1

6 0
1 year ago
Other questions:
  • M is directly proportional to r2.when r=2,m=14.Work out the value of m when r=12
    11·1 answer
  • Out of 1,000 people in a small town, 500 are members of a choir. Out of these 500 members in a choir, 100 are men. Out of the 50
    15·2 answers
  • What is the square root of 1350÷600
    14·1 answer
  • Evaluate the expression 7!/4!
    8·1 answer
  • How many solutions does this equation have?
    15·2 answers
  • Choose one answer please help me
    15·1 answer
  • Help please <br> Brainiest answer to whoever is first
    15·1 answer
  • Write AND Solve the expression. <br><br> Subtract 10 from 24 then add the product of 3 and 7
    5·1 answer
  • A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 22 kilograms each, and the small box
    6·1 answer
  • How to solve hcf a^2+5a+6<br>​
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!