Question

If $f(x)=\frac{2x+1}{3x-2},$ then $(fof)(2)$ is equal to:

• A. 1
• B. 3
• C. 4
• D. 2
• E. none of these

Answer 1

Answer: (D)

$\because$ $f(x)=\frac{2x+1}{3x-2}$ $\therefore$ $f(2)=\frac{4+1}{4}=\frac{5}{4}$ $fof(2)=f\{f(2)\}=f\left(\frac{5}{4}\right)$ $=\frac{2\left(\frac{5}{4}\right)+1}{3\left(\frac{5}{4}-2\right)}=\frac{\frac{5+2}{2}}{\frac{15-8}{4}}=\frac{14}{7}=2$