we have the equations
[tex]\begin{gathered} f(x)=\frac{x+1}{x^2} \\ \\ g(x)=\frac{x-1}{x+1}+1 \end{gathered}[/tex]
equate both equations
[tex]\frac{x+1}{x^2}=\frac{x-1}{x+1}+1[/tex]
First iteration
For x=1
[tex]\begin{gathered} \frac{1+1}{1^2}=\frac{1-1}{1+1}+1 \\ \\ 2=1 \end{gathered}[/tex]
For x=2
[tex]\begin{gathered} \frac{2+1}{2^2}=\frac{2-1}{2+1}+1 \\ \\ \frac{3}{4}=\frac{1}{3}+1 \\ \\ \frac{3}{4}=\frac{4}{3} \\ 0.75=1.33 \end{gathered}[/tex]
For x=1.5
[tex]\begin{gathered} \frac{1.5+1}{1.5^2}=\frac{1.5-1}{1.5+1}+1 \\ \\ \frac{\frac{5}{2}}{\frac{9}{4}}=\frac{\frac{1}{2}}{\frac{5}{2}}+1 \\ \\ \frac{20}{18}=\frac{1}{5}+1 \\ \frac{10}{9}=\frac{6}{5} \\ 1.11=1.2 \end{gathered}[/tex]
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
