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]
3 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]3 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]3 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
Write all names that apply to the number 36/9
rjkz [21]
Whole number
integer
natural number
rational
4 0
3 years ago
Someone please help with this proof
Novosadov [1.4K]
Easy so you have to choose them then add them and yeah hope this helps bbg
7 0
3 years ago
Suppose y varies directly with x. If y = 6 when x = 2, find x when y = 12. 4 3
kobusy [5.1K]

\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \textit{we also know that } \begin{cases} y=6\\ x=2 \end{cases}\implies 6=k(2)\implies \cfrac{6}{2}=k\implies 3=k \\\\\\ therefore\qquad \boxed{y=3x} \\\\\\ \textit{when y = 12, what is \underline{x}?}\qquad 12=3x\implies \cfrac{12}{3}=x\implies 4=x

6 0
3 years ago
6×1(4+7)÷8×19(7-13)<br><br>solve and the correct answer wins the Brainlist​
alukav5142 [94]

Answer:

-940.5

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Please help im beggih
Lana71 [14]
Number 17 is A and18 is F
7 0
3 years ago
Other questions:
  • 0.6(10m-5n) do you know this
    10·1 answer
  • Convert to an improper fraction. Type in your answer with the negative in the numerator. -12 3/4
    13·2 answers
  • Whats 1.02 as a fraction
    10·2 answers
  • Somebody please help me. I cant figure this out once so ever.
    9·1 answer
  • Find the two square roots of 144.
    13·2 answers
  • Find the ratio if it is given that ...
    9·2 answers
  • *** SOMEBODY HELP ME**
    12·1 answer
  • The sum of three consecutive number is 63 find the number​
    14·1 answer
  • What’s the slope of the black line
    5·1 answer
  • Solve using elimination.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!