For the following exercises, find the domain of the rational functions. f(x)=\frac{x^{2}+4}{x^{2}-2x-8}

Tahmid Knox

Tahmid Knox

Answered question

2021-09-24

For the following exercises, find the domain of the rational functions. f(x)=x2+4x22x8

Answer & Explanation

Margot Mill

Margot Mill

Skilled2021-09-25Added 106 answers

1. Function:
f(x)=x2+4x22x8
2. For a function that is defined by a fraction, the function is undefined when its denominator is equal to 0, therefore equate the denominator with 0 to evaluate the value of x for which the function will be undefined:
x22x8=0
Factor using ac method: x2+2x4x8=0
Factor: (x+2)(x-4)=0
Now equate each factor with 0 and solve for the variable, therefore: x=-2
x=4
Therefore, it can be concluded that the domain of the function are all real numbers except x=-2 and x=4.

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