The value of the 4th iterate of the given function f(x) is -2.096
2nd option is correct.
A function's iterate is a function that is expressed as repetition of another (already iterated) function; this latter function may be referred to as the iterand.
Any function taken on its own is regarded as the first iteration.
A function is said to have an identity function at iteration zero.
According to the question,
f(x) = (3x-1)/[tex]x^{2}[/tex]
[tex]x_{o}[/tex] = -2
The first iterate is calculated by finding f(-2).
f(-2) = (3(-2)-1)/4
f(-2) = -1.75
Similarly, the next iterates are calculated as follows:
f(-1.75) = -2.048
f(-2.048) = -1.71
f(-1.71) = -2.096
Thus, the fourth iterate for the given function is [tex]x_{4}[/tex]= -2.096
Learn more about iterates here:
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