The domain of this function is all the real numbers except - 7 / 3 and 23 / 3.
What is the domain of a function?
In accordance with function theory, the domain of a function is a set of x-values such that y-values exist. Herein we find that the given function is a rational function whose denominator includes an absolute value function. The numerator is a linear equation.
Therefore, the domain of the function is all real numbers except those x-values such that denominator is equal to zero. We need to solve the following expression in two cases:
|3 · x - 15| = 8
For x ≥ 5:
3 · x - 15 = 8
3 · x = 23
x = 23 / 3
For x < 5:
- 3 · x + 15 = 8
- 3 · x = - 7
x = - 7 / 3
Then, the domain of this function is all the real numbers except - 7 / 3 and 23 / 3.
To learn more on rational functions: https://brainly.com/question/27914791
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