Answer:
The solutions to the equation f(x) = g(x) are approximately -4.59, -4.36, 2.11, and 2.84.
Explanation:
To solve the eqation f(x) = g(x), we need to set the expressions for f(x) and g(x) equal to each other and solve for x. However, since g(x) involves an absolute value, we will need to consider two cases: one where 0.6x is positive, and one where it is negative.
Case 1: 0.6x is positive
In this case, we can write the equation as:
-0.25x³ - x² + 1.3x - 1.8 = 0.6x - 7.7
Simplifying, we get:
-0.25x³ - x² + 0.7x + 5.9 = 0
We can solve this equation using numerical methods, such as graphing or using a calculator, to find that x ≈ -4.59 and x ≈ 2.84.
Case 2: 0.6x is negative
In this case, we can write the equation as:
-0.25x³ - x² + 1.3x - 1.8 = -0.6x - 7.7
Simplifying, we get:
-0.25x³ - x² + 1.9x + 5.9 = 0
Again, we can use numerical methods to solve this equation and find that x ≈ -4.36 and x ≈ 2.11.
Therefore, the solutions to the equation f(x) = g(x) are approximately -4.59, -4.36, 2.11, and 2.84.