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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.

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Question 3
alexira [117]

Answer: when x = 7, y = 16

Step-by-step explanation: Here, we know that y varies inversely as x.

When we have two sets of inversely related coordinates, x₁ and y₁,

and x₂ and y₂, we can use the product rule, shown below,

to find the missing value.

<h2>x₁ y₁ = x₂ y₂</h2><h2 />

Here, we know that y = 14 when x = 8 so

one set of coordinates will be 8 and 14.

We want to know the value of y when x = 7.

So our other coordinates will be 7 and y.

So we have (8)(14) = (7)(y).

Simplifying, (8)(14) is equal to 112 and (7)(y) is equal to 7y.

So we have 112 = 7y.

Now we simply solve for y by dividing both sides of the equation by 7.

The 7's on the right side cancel out and

on the left, 112 divided by 7 is equal to 16.

So we have 16 = y.

So when x is equal to 7, y is equal to 16.

7 0
3 years ago
Which of the following numbers is irrational?
baherus [9]
An irrational number is one that can’t be expressed as a simple fraction.

For instance, the first few digits of the square root of two is written as 1.414213562373095... The digits keep going and cannot be expressed as a fraction. But think of 0.33333... That can easily be written as one-third. The distinguishing feature is that there’s no pattern in the digits for the square root of two.

The first two options are integer fractions. We rule those out immediately. The square root of four is tempting, but realize that it is just equal to two. We come to π (pi).

Arguably the most famous irrational number is π, which starts off as 3.14159265358979... Here, there is again no pattern and the digits extend forever. This meets our definition of our irrational.
8 0
3 years ago
Read 2 more answers
Please help
pav-90 [236]

Answer:

Step-by-step explanation:

Just stop taking 40 dollars out of the bank every week

7 0
3 years ago
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Mr. Kevin pays $37.95 per month for his cell phone with unlimited minutes. At this rate, what will his cellphone
masya89 [10]
$37.95 x12= 455.4 so Kevin’s cellphone will cost 455.4 for the year
5 0
3 years ago
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In NC, Henderson County has a land area of about 375 square miles and Perquimans County has a land area of about 250 square mile
kirza4 [7]

375 mi^2         15

--------------- =  ------ = 3/2

250 mi^2        10

The ratio of the population of Henderson County to that of Perquimans is 3/2.

4 0
2 years ago
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