The domain of a function are the possible x-values. The domain of function g(x) is [tex](-\infty, \infty)[/tex]
Given
[tex]g(x) = \left[\begin{array}{ccc}\frac{x^2 +2x }{x^2 + x - 2}&, \ x<2\\\log_2(x + 2) &x \ge 2\end{array}\right[/tex]
From the function, the possible values of x are:
[tex]x < 2[/tex] and [tex]x \ge 2[/tex]
[tex]x < 2[/tex] means that the values of x are [tex](-\infty, 2)[/tex]
[tex]x \ge 2[/tex] mean that the values of x are [tex][2, \infty)[/tex]
These values can be combined as follows:
[tex](-\infty, 2) + [2, \infty) = (-\infty, \infty)[/tex]
Hence, the domain of the function is: [tex](-\infty, \infty)[/tex]
Read more about domains at:
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