Answer :

The domain of the function is the set of all real numbers and the range is the set of non-negative real numbers.

How to find the domain of a function

The domain of a function is the set of x-values such that the function exists. Herein we find a rational equation involving absolute values. Both the numerator and the denominator have forms of linear equations and we can infer that the domain of f(x) is all the real numbers except the values of x such that |x - 5| = 0.

However, it seems that the discontinuity is evitable:

2 · (x - 5) / |x - 5|                              Given

2 · (x - 5) / (x - 5)                              Definition of absolute value

2                                                       Defintion of division / Existence of absolute value / Associative and modulative properties / Result

Then, the domain of the function is all the real numbers. And given the presence of linear equations and absolute values, the range of the function are all the non-negative real numbers.

To learn more on domain and range of functions: https://brainly.com/question/28135761

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