For the following exercises, find the domain of the rational functions. f(x)=\frac{x^{2}+4x-3}{x^{4}-5x^{2}+4}

CMIIh

CMIIh

Answered question

2021-05-09

For the following exercises, find the domain of the rational functions.
f(x)=x2+4x3x45x2+4

Answer & Explanation

tabuordy

tabuordy

Skilled2021-05-10Added 90 answers

Function: 
f(x)=x2+4x3x45x2+4 
2. In order to determine the value of « for which the function will be undefined, equate the denominator with 0: For a function that is defined by a fraction, the function is undefined when its denominator is equal to 0:
x45x2+4=0 
Factor using ac method: 
x4x24x2+4=0 
Write as factors: (x41)(x24)=0 
Each of these factors can further be factored using difference of squares method, therefore: 
(x-1)(x+1)(x-2)(x+2)=0 
Now equate each factor with 0 and solve for the variable, therefore: 
x=-2 
x=-1 
x=1 
x=2 
Therefore, it can be concluded that the domain of the function are all real numbers except x=-2,x=-1,x=1 and x=2.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?