The set of inequalities y ≤ x² - 3 and y > -x² + 2 do not have a solution
<h3>How to modify the graphs</h3>The attached figure 1 represents the missing piece in the question
From the graph, we have:
f(x) = x² - 3
g(x) = -x² + 2
Next, we change the equations to inequalities as follows:
y ≤ x² - 3
y > -x² + 2
To modify the graph, we then perform the following transformations:
- Shift the function g(x) down by 2 units
- Reflect across the x-axis
- Shift the function g(x) down by 3 units
After the modifications in (a), we have:
y ≤ x² - 3 and y > -x² + 2
Next, we plot the graph of the inequalities
From the graph of the inequalities, the curves of the inequalities have no point of intersection
Hence, the set of inequalities do not have a solution
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