Each function operation should be matched with what it is equivalent to as follows:
f(x) + g(x) = -2x² + x + 6.
g(x) - f(x) = -2x² - 5x + 2.
f(x) · g(x) = -6x³ - 10x² + 8x + 8.
h(x) - f(x) = 3x² - 7x - 2
f(x) · h(x) = 9x³ - 6x² - 8x.
f(x) + g(x) + h(x) = x² - 3x + 6.
<h3>How to determine the solutions of the given function?</h3>
In order to determine the solutions of the given function, we would have to evaluate each of the function based on the required mathematical operations as follows.
From the information provided, we have the following functions:
f(x) = 3x + 2
g(x) = -2x² - 2x + 4
h(x) = 3x² - 4x
f(x) + g(x) = 3x + 2 + (-2x² - 2x + 4)
f(x) + g(x) = 3x + 2 - 2x² - 2x + 4
Next, we would rearrange the function by collecting like terms as follows:
f(x) + g(x) = -2x² + (3x - 2x) + (2 + 4)
f(x) + g(x) = -2x² + x + 6 (solution).
g(x) - f(x) = -2x² - 2x + 4 - (3x + 2)
Opening the bracket, we have:
g(x) - f(x) = -2x² - 2x + 4 - 3x - 2
Next, we would rearrange the function by collecting like terms as follows:
g(x) - f(x) = -2x² + (-2x - 3x) + (4 - 2)
g(x) - f(x) = -2x² - 5x + 2 (solution).
f(x) · g(x) = (3x + 2) × (-2x² - 2x + 4)
Opening the bracket, we have:
f(x) · g(x) = -6x³ - 6x² + 12x - 4x² - 4x + 8
Next, we would rearrange the function by collecting like terms as follows:
f(x) · g(x) = -6x³ + (-6x² - 4x²) + (12x - 4x) + 8
f(x) · g(x) = -6x³ - 10x² + 8x + 8 (solution).
h(x) - f(x) = 3x² - 4x - (3x + 2)
h(x) - f(x) = 3x² - 4x - 3x - 2
h(x) - f(x) = 3x² - 7x - 2 (solution).
f(x) · h(x) = (3x + 2) × (3x² - 4x)
f(x) · h(x) = 9x³ - 12x² + 6x² - 8x
f(x) · h(x) = 9x³ - 6x² - 8x (solution).
f(x) + g(x) + h(x) = 3x + 2 + (-2x² - 2x + 4) + (3x² - 4x)
f(x) + g(x) + h(x) = -2x² + x + 6 + 3x² - 4x
f(x) + g(x) + h(x) = x² - 3x + 6 (solution).
Read more on function here: brainly.com/question/3632175
#SPJ1
