Based on the calculations, the fourth (4) iterations of the given function is equal to: A. x₄ = -2.096.
In this exercise, you're required to find the fourth (4) iterations of the given function. Thus, we would substitute the value of x₀ into the function and then evaluate as follows:
First iteration:
f(x) = (3x - 1)/x²
f(x₀) = (3x - 1)/x₀²
f(-2) = (3(-2) - 1)/(-2)²
f(-2) = -7/4
f(-2) = -1.75.
Second iteration:
f(x) = (3x - 1)/x²
f(x₁) = (3x - 1)/x₁²
f(-1.75) = (3(-1.75) - 1)/(-1.75)²
f(-1.75) = -6.25/3.0625
f(-1.75) = -2.04.
Third iteration:
f(x) = (3x - 1)/x²
f(x₂) = (3x - 1)/x₂²
f(-2.049) = (3(-2.04) - 1)/(-2.04)²
f(-2.04) = -7.12/4.1616
f(-2.04) = -1.71.
Fourth iteration:
f(x) = (3x - 1)/x²
f(x₃) = (3x - 1)/x₃²
f(-1.71) = (3(-1.71) - 1)/(-1.71)²
f(-1.71) = -6.13/2.9241
f(-1.71) = -2.096.
x₄ = -2.096.
Read more on iteration here: https://brainly.com/question/14828536
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