Question

Find the first 3 interations here: g(x)=-1|x-2|+3 if you have an initial value of 0.5

Answer 1

Answer:

• The first iteration = 1.5

• The 2nd iteration = 2.5

• The third iteration = 2.5

Step-by-step explanation:

Considering the function

• $g\left(x\right)=-1\:|\:x\:-\:2\:|\:+\:3$

• As the initial value = 0.5

• In order to determine the next iterate, apply the function g(x) to the previous one.

DETERMINING FIRST ITERATION:

$g\left(0.5\right)=-1\:|\:0.5\:-\:2\:|\:+\:3$

          = -1 | 0.5 - 2 | + 3

          = -1 | -1.5 | + 3

$\mathrm{Apply\:absolute\:rule}:\quad \left|-a\right|=a$ ; | -1.5 | =  1.5

          $=-1.5+3$  

          = 1.5

Thus, the first iteration = 1.5

DETERMINING SECOND ITERATION:

Putting the value of first iteration i.e. 1.5 into the original function to determine the 2nd iteration.

$g\left(1.5\right)=-1\:|\:1.5\:-\:2\:|\:+\:3$

as    $1.5 - 2 = -0.5$

$\mathrm{Apply\:absolute\:rule}:\quad \left|-a\right|=a$ ;  | -0.5 | =  0.5

        $=-0.5+3$

        = 2.5

Thus, the 2nd iteration = 2.5

DETERMINING THIRD ITERATION:

Putting the value of second iteration i.e. 2.5 into the original function to determine the 2nd iteration.

$g\left(2.5\right)=-1\:|\:2.5\:-\:2\:|\:+\:3$

$\mathrm{Apply\:absolute\:rule}:\quad \left|a\right|=a,\:a\ge 0$

         $=-0.5+3$        as  $2.5-2=0.5$

         = 2.5

Thus, the third iteration = 2.5