Finding the Domain and Solving an Equation with Rational Functions

  • Thread starter Thread starter Quisquis
  • Start date Start date
AI Thread Summary
The discussion focuses on determining the domain of the rational function f(x) = (3x + 4) / (2x + 9) and solving the equation y = f(x) for x. The initial confusion arises from understanding that the "largest set of real numbers" refers to the function's domain, which excludes values that make the denominator zero. After attempts to manipulate the equation, the user receives advice to isolate x by moving terms and factoring. Following this guidance, the user successfully solves the equation after further effort. The exchange highlights the importance of clearing denominators and rearranging terms in solving rational functions.
Quisquis
Messages
52
Reaction score
0
1. The problem, as stated:

What is the largest set of real numbers on which the function whose rule is f(x)=\frac{3x+4}{2x+9} can be defined? Solve the equation y=f(x) for x.

2. The attempt at a solution

I've done the first part of the equation after realizing that "...the largest set of real numbers..." just meant the domain, but I've really got no idea what to do with the last part.

I've tried multiplying the top and bottom by the denominator... multiplying both sides to clear out the denominator. A bunch of different stuff that doesn't seem to get me anywhere.

I would really appreciate it if I could get some help as to where to go with this.

-Quisquis
 
Physics news on Phys.org
After clearing denominators, try to move the terms with an x to one side and the other terms to the other side. Then factor out an x and divide.
 
After like 20 more minutes of messing with it after your advice, I figured it out.

Thanks a lot. :biggrin:
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
View full post »

Thread 'Making the denominator of a certain fraction real'

Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...
View full post »

Similar threads

Finding the domain of a composite function
Replies
10
Views
2K
To find the range of a given ##\sin## function
Replies
15
Views
2K
How to identify the type of function?
Replies
23
Views
3K
To find the boundedness of a given function
Replies
14
Views
3K
Finding a domain for a function
Replies
7
Views
2K
State the domain and range for a given function
Replies
7
Views
2K
Is ##f(x)=2^{x}-1## considered an exponential function?
Replies
12
Views
2K
Domain and Range of a Function and Its Inverse- Polynomials
Replies
9
Views
2K
Transforming Piecewise Functions
Replies
3
Views
2K
Rational expressions and domains
Replies
5
Views
2K

Hot Threads

Recent Insights

Back
Top