Chapter 11, Problem 53SGR

To determine

Find the first three iterates of the function $f(x)=6x-1$ for the given initial value $x_0=2$

Answer to Problem 53SGR

  $x_1=11;x_2=65;x_3=389$

Explanation of Solution

Given:

The function and the initial value: $f(x)=6x-1;x_0=2$

Concept Used:

The function and the initial value: $f(x)=6x-1;x_0=2$

Calculation:

  $f(x)=6x-1;x_0=2$

Plug in $x_0=2$ to find $x_1$ .

  $\begin{array}{l}f(x)=6x-1;x_0=2\\ x_1=f(x_0)=f(2)=6(2)-1=11\\ x_1=11\end{array}$

Repeat the process by plugging in the answer you got for $x_1=11$

  $f(x)=6x-1;x_1=11$

  $\begin{array}{l}{x}_2=f(x_1)=f(11)=6(11)-1=65\\ x_2=65\end{array}$

Repeat the process by plugging in the answer you got for $x_2=65$

  $f(x)=6x-1;x_2=65$

  $\begin{array}{l}{x}_3=f(x_2)=f(65)=6(65)-1=389\\ x_3=389\end{array}$

Thus, $x_1=11;x_2=65;x_3=389$