Question

How do you find the first three iterate of the function `f(x)=3x+5` for the given initial value `x_0=-4`?

Answer 1

`(x_1,x_2,x_3)=(-7,-16,-43)`

Explanation:

|'ve never actually seen it expressed in this form but what I assume is meant by the iterations is:
`color(white)("XXX")x_1=f(x_0)`
`color(white)("XXX")x_2=f(x_1)`
`color(white)("XXX")x_3=f(x_2)`
...and so on

If this is the case, then given `f(x)=3x+5` and `x_0=-4`,
we have:
`color(white)("XXX")x_1=f(-4) = 3 * (-4) + 5 = -12+5=-7`
`color(white)("XXX")x_2=f(-7)=3 * (-7)+5=-21+5=-16`
`color(white)("XXX")x_3=f(-16)=3 * (-16)+5=-48+5 = -43`