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

1 Answer
Jan 22, 2017

#(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#