Answer:
The correct option is;
D. F(x) = x⁴ - x² + 2
Step-by-step explanation:
From the graph, we have;
The y-intercept = 2, therefore, when x = 0, y = 2
The graph has no x-intercept, therefore, the unction has complex roots
The possible function is F(x) = x⁴ + x² + 2 and F(x) = 2 - x⁴ - x²
The roots of the function, F(x) = x⁴ - x² + 2, is given as follows;
0 = x⁴ - x² + 2
x = (1 ± √(1 - 8))/(2) = (1 ± √(-7))/(2) which are imaginary roots
For F(x) = 2 - x⁴ - x², we have;
0 = 2 - x⁴ - x²
x = (1 ± √(1 + 8))/(2) = (1 ± 3)/(2)
x = 2 or x = -1, therefore, the function, F(x) = 2 - x⁴ - x², has real roots and the only possible solution is F(x) = x⁴ + x² + 2
