The x-intercepts of the piecewise function are 1.59 and 17 and the intervals where g(x) is positive are (-2,0) and [2,17)
<h3>The graph of the function</h3>
The piecewise function is given as:
![g(x) = \left[\begin{array}{cc}x^3-4x &x < 2\\-\log_4(x - 1) + 2 &x \ge 2\end{array}\right](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dx%5E3-4x%20%26x%20%3C%202%5C%5C-%5Clog_4%28x%20-%201%29%20%2B%202%20%26x%20%5Cge%202%5Cend%7Barray%7D%5Cright)
See attachment for the graph of the piecewise function.
<h3>The x-intercepts of the
piecewise function</h3>
This is the point where the piecewise function crosses the x-axis.
From the attached graph, the graph crosses the x-axis at x = -2, x = 0 and x = 17
Hence, the x-intercepts of the piecewise function are -2, 0 and 17
<h3>The intervals where g(x) is positive</h3>
This is the range of x value where g(x) > 0
From the attached graph, g(x)> 0 between x = -2 & x = 0 and between x = 2 (inclusive) & x = 17
Hence, the intervals where g(x) is positive are (-2,0) and [2,17)
Read more about piecewise function at:
brainly.com/question/11827078
#SPJ1