Find the Function G for Given F(x) = 1/x and (f/g)(x) = (x+1)/(x^2-x)

In summary, the function g(x) is (x-1)/(x+1) and it is found by dividing 1/x by the given function (x+1)/(x^2-x).
  • #1
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Q) Given F(X) = 1/x and (f/g)(x) = (x+1)/(x^2-x). find the function g.

A: (x+1)/x(x-1) = (1/x) . (x+1)/(x-1)

Hence, the function G is (x+1)/(x-1)


Is this answer correct?
 
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  • #2
Almost! You have shown that [itex]\frac{x+1}{x^2- x}= \frac{x+1}{x(x-1)}= \frac{1}{x}\left(\frac{x+1}{x-1}\right)= f(x)\left(\frac{x+1}{x-1}\right)[/itex] correctly.

But you want f/g, not f*g! How do you divide by a fraction?
 
  • #3
So that would be (1/x) / (x+1)(x-1) = (x-1) / ( x^2+x)

Is that the correct answer?


thanks
 
  • #4
Nope, that's still wrong. You can recheck your calculation.
g(x) = f(x) / ((f / g)(x))
By the way, at your first post, it reads F(x) = 1 / x. Do you really mean that or f(x) = 1 / x?
Viet Dao,
 
  • #5
What I wrote before was
[tex]\frac{x+1}{x^2- x}= \frac{x+1}{x(x-1)}= \frac{1}{x}\left(\frac{x+1}{x-1}\right)= f(x)\left(\frac{x+1}{x-1}\right)= \frac{f(x)}{g(x)}[/tex]

So [tex]\frac{1}{g(x)}= \frac{x+1}{x-1}[/tex].

Now do you see what g(x) is?

Once again, how do you divide by a fraction?
 
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  • #6
damn... So does g(x) = (x-1)/(x+1) ?



By the way, at your first post, it reads F(x) = 1 / x. Do you really mean that or f(x) = 1 / x?

I mean, f(x)=1/x
 
Last edited:
  • #7
Yup. That's correct.
Viet Dao,
 

What is a function?

A function is a mathematical relationship between two variables, where the output (dependent variable) is determined by the input (independent variable) through a set of rules or equations.

What is the purpose of doing function homework?

The purpose of doing function homework is to help students understand the concept of functions and how they can be used to solve problems in math and science. It also helps students practice their skills in identifying, graphing, and manipulating different types of functions.

How do I graph a function?

To graph a function, you need to first determine the domain and range of the function. Then, plot points on a coordinate plane using the input and output values. Finally, connect the points to create a smooth curve that represents the function.

What are some real-life applications of functions?

Functions have many real-life applications, such as predicting the growth of a population, calculating compound interest, and modeling the trajectory of a projectile. They are also used in fields like engineering, economics, and physics to solve various problems and make predictions.

How can I improve my understanding of functions?

To improve your understanding of functions, it is important to practice solving different types of function problems, such as finding the domain and range, graphing functions, and solving equations involving functions. It is also helpful to seek assistance from a teacher, tutor, or online resources for additional explanations and examples.

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