The question asks for the solutions of the function $g(x) = -x^4 + 6x^2 - 8$ at certain points, based on the provided graph.

Steps to Solve:

1. Identify where $g(x) = -2$ on the graph:

   • We need to find the x-values where the function reaches the value of -2 on the y-axis (i.e., $g(x) = -2$).
   • This corresponds to the points where the horizontal line $y = -2$ intersects the curve.

2. Interpreting the Graph:

   • From the graph, the curve intersects $y = -2$ at two points:
     • One near x = -2.
     • One near x = 2.

3. Checking the Options:

   • From the possible choices:
     • The correct pair of solutions appears to be $x = -2$ and $x = 2$.

Answer:

• The correct option is: $x = -2$ and $x = 2$.

Do you have any further questions, or need detailed steps?

Here are 5 related questions for more practice:

1. What is the degree of the polynomial $g(x) = -x^4 + 6x^2 - 8$?
2. How do the roots of a polynomial relate to its graph's x-intercepts?
3. What happens to the graph of a function when the leading coefficient is negative?
4. How do you determine the maximum or minimum points of a polynomial function?
5. What does the multiplicity of a root tell us about the shape of the graph at that root?

Tip: When solving for roots or specific values of a function, look carefully at the intersections of the graph with horizontal lines!