A) \[1\]
B) \[3\]
C) \[4\]
D) \[2\]
Correct Answer: D
Solution :
Given that \[f(x)=\frac{2x+1}{3x-2}\] \[\therefore \] \[fof(x)=f(f(x))\] \[=\frac{2\left( \frac{2x+1}{3x-2} \right)+1}{3\left( \frac{2x+1}{3x-2} \right)-2}\] \[=\frac{4x+2+3x-2}{6x+3-6x+4}\] \[=\frac{7x}{7}=x\] \[\Rightarrow \] \[fof(2)=2\] Alternate Solution: Since, \[f(x)=\frac{2x+1}{3x-2}\] Now, \[f(2)=\frac{2\times 2+1}{3\times 2-2}=\frac{5}{4}\] \[\therefore \] \[fof(2)=f(f(2))\] \[=f\left( \frac{5}{4} \right)=\frac{2\times \frac{5}{4}+1}{3\times \frac{5}{4}-2}\] \[=\frac{\frac{10}{4}+1}{\frac{15}{4}-2}=\frac{14}{7}\] \[=2\]
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