Problem composing a rational function with itself.

• fedaykin
In summary, the conversation is about composing f(x)= x + \frac{1}{x} with itself and the incorrect answer that was obtained by multiplying \frac{1}{x + (1/x)} * \frac{x}{x} and the correct answer from the book, \frac{x^4+3x^2+1}{x(x^2+1)}. The expert also mentions the importance of using a common denominator and wishes the other person good luck on their exam.
fedaykin
I'm trying to compose $$f(x)= x + \frac{1}{x}$$ with itself. e.g. $$f \circle f$$

I have $$x + \frac{1}{x} + \frac{1}{x+(1/x)}$$

Now I multiplied $$\frac{1}{x + (1/x)} * \frac{x}{x}$$ and I got:

$$x + \frac{1}{x} + \frac{x}{x^2+1}$$

This is not the correct answer according to the book.
Books is:

$$\frac{x^4+3x^2+1}{x(x^2+1)}$$

I have no idea how they got that. I can't get a common denominator and get that.

Last edited:
Try a forward slash on the final [tex]. But your answer is also correct. Put everything over a common denominator of x*(x^2+1).

Thank you very very very much. My first 100 in calc so far awaits me tomorrow!

Good luck!

1. What is a rational function?

A rational function is a function that can be written as a ratio of two polynomials. In other words, it is a fraction where the numerator and denominator are both polynomials.

2. How do you compose a rational function with itself?

To compose a rational function with itself, you simply plug the original function into itself. In other words, you replace all instances of the variable in the original function with the entire function.

3. What is the purpose of composing a rational function with itself?

The purpose of composing a rational function with itself is to create a new function that may have different properties or behaviors than the original function. This can be useful in solving certain mathematical problems or in creating new functions for specific purposes.

4. Is it possible to compose any rational function with itself?

Yes, it is possible to compose any rational function with itself. However, the resulting function may not always be defined for all values of the variable, so it is important to check for any restrictions or limitations on the domain.

5. How can composing a rational function with itself help in solving problems?

Composing a rational function with itself can help in solving problems by creating a new function that may have simpler or more desirable properties. This can make it easier to find the roots, intercepts, or asymptotes of the function, or to analyze its behavior and make predictions about its graph.

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