Question

i need help with this asap Consider the following equations.Approximate the solution to the equation f(x) = g(x) using three iterations of successive approximation. Use the graph below as a starting point.

Answer 1

we have the equations

`\begin{gathered} f(x)=(x+1)/(x^2) \\ \\ g(x)=(x-1)/(x+1)+1 \end{gathered}`

equate both equations

`(x+1)/(x^2)=(x-1)/(x+1)+1`

First iteration

For x=1

`\begin{gathered} (1+1)/(1^2)=(1-1)/(1+1)+1 \\ \\ 2=1 \end{gathered}`

For x=2

`\begin{gathered} (2+1)/(2^2)=(2-1)/(2+1)+1 \\ \\ (3)/(4)=(1)/(3)+1 \\ \\ (3)/(4)=(4)/(3) \\ 0.75=1.33 \end{gathered}`

For x=1.5

`\begin{gathered} (1.5+1)/(1.5^2)=(1.5-1)/(1.5+1)+1 \\ \\ ((5)/(2))/((9)/(4))=((1)/(2))/((5)/(2))+1 \\ \\ (20)/(18)=(1)/(5)+1 \\ (10)/(9)=(6)/(5) \\ 1.11=1.2 \end{gathered}`

the answer must be less than 1.5 and greater than 1

so

Verify each option

A ----> 13/8=1.625 -----> is not a solution

B ----> 23/16=1.4375 ---> could be an approximate solution

C ---> 25/16=1.5625 ----> is not a solution

D ---> 7/4=1.75 ----> is not a solution

therefore

The answer is option B