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
Yuki888 [10]
3 years ago
7

Let $f(x)$ be the real-valued function defined for all real $x$ except for $x = 0$ and $x = 1$ and satisfying the functional equ

ation \[f(x) + f\left(\frac{x-1}x\right) = 1+x.\]find the $f(x)$ satisfying these conditions. write $f(x)$ as a rational function with expanded polynomials in the numerator and denominator.

Mathematics
1 answer:
Mademuasel [1]3 years ago
7 0
We have to find the values of F.
In this case. F is unlikely to be a polynomial.
But the problem is, we can’t calculate the values of F directly.
There is no real value of x for which x = x−1 x because F isn’t defined at 0 or 1. so,
substituting x = 2.
F(2) + F(1/2) = 3.

Substitute, x = 1/2
F(1/2) + F(−1) = −1/2.
We still are not getting the required value,
therefore,
Substitute x = −1

As, F(2) +F(−1) = 0.
now we have three equations in three unknowns, which we can solve.
It turns out that:
F(2) = 3/4
F(3) = 17/12
F(4) = 47/24
and
F(5) = 99/40

Setting
g(x) = 1 − 1/x
and using
2 → 1/2
to denote
g(2) = 1/2
 we see that :
x → 1 - 1/x → 1/(1-x) →x

so that:
g(g(g(x))) = x.

Therefore, whatever x 6= 0, 1 we start with, we will always get three equations in the three “unknowns” F(x), F(g(x)) and F(g(g(x))).
Now solve these equations to get a formula for F(x)

As,
h(x) = (1+x)/(1−x)
which satisfies h(h(h(h(x)))) = x

Now, mapping x to h(x) corresponds to rotating the circle by ninety degrees.

You might be interested in
HELP!! Given f(x)=5x squared and g(x) = x squared + 2x squared - 5x, what is F (x) * g(x)?
TEA [102]
X^2+2x^2-5x

((x^2)+2x^2)-5x

Pull the factors out

3x^2-5x=x(3x-5)

x(3x-5)

x(3x-5)*5x^2

5x(3x-5)*x^2


Final

5x^3*(3x-5)



8 0
3 years ago
An 18 ounce box of cereal costs $2.76. How many ounces should a box priced at $2.07 contain?
Darya [45]
First you find the unit rate. (Divide 2.76 by 18)
You will find out that each ounce costs $0.15

Then divide 2.07 by 0.15.

The answer is 13.8 ounces.

5 0
3 years ago
How to divide 33 photos into two groups so that the ratio is 4 to 7
velikii [3]
The ratio 4 to 7. would be 12 and 21
5 0
3 years ago
Graph each equation.<br><br> y=-2x-1 <br><br> help please
yan [13]
You can graph that by looking at the y-intercept first. That's where you start to put a point in the coordinate plane or graph.

So go down 1 below 0.

Next, look at the slope.
We know that y = -2x - 1 is in slope intercept form (y = mx+b)
So -2 is our slope. It will be -2/1 because we need a fraction to graph the rise over run and all whole numbers can be a fraction by making 1 as their denominator.

Look at the attachment. 

Starting from -1 (y-intercept), go down 2 (-2) then right 1 (1).
To complete the line above, keep the same value and reverse their sign/symbol. So -2/1 will be 2/-1. It goes up 2 then left 1.

I hope you understand and find this answer the most helpful! :)

8 0
3 years ago
It is greater than 43 and less then 52 if you add the digits the sum is 8
Ksenya-84 [330]
44 is the answer 4+4=8
3 0
3 years ago
Other questions:
  • Whst is the answer to 1 3/4 - 7/10 = ?
    5·2 answers
  • Ahmad runs 6 miles in 45 minutes. At the same rate, how many minutes would he take to run 4 miles?
    8·2 answers
  • a rectangular sheet of metal is 250 cm wide and has a diagonal of 472cm. Find the length and the area of the sheet metal.
    7·1 answer
  • What is the value 7?
    13·1 answer
  • Bob paid $18.00 for a pair of shorts that were 20% off. What was the original price?? Show all steps...please.....
    10·2 answers
  • The Greenville youth football team bought new footballs for their practices. They bought 9 footballs for a total of $130.50. How
    13·2 answers
  • Carl buys seven 5-gallon jugs of water for the water cooler. How many liters of water did Carl buy? Show your work.
    6·1 answer
  • Find the difference,
    12·2 answers
  • Find the greatest common factor of 7 and 7
    10·2 answers
  • Find the domain, vertical asymptotes, and horizontal asymptotes of the function.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!