Question

help me with this question​

Answer 1

Answer:

fof(x) = x

fof(2) = 2

option (D) is correct.

Answer 2

$Given \: \: Question \: \: Is \: \\ \\ If \: \: \: \: f(x) = \frac{2x + 1}{3x - 2} \: \: \: \: then \: \: \: (fof)(2)\\ \\ Answer \: \\ \\f(x)= \frac{2x + 1}{3x - 2} \\ \\ put \: \: x = 2 \\ \\ f(2)) = \frac{2(2) + 1}{3(2) - 2} \\ \\ f(2) = \frac{4 + 1}{6 - 2} \\ \\ f(2) = \frac{5}{4} \\ \\ Now \: \: (fof)(2) = f(f(2) \\ \\ replace \: \: x\: \: \: by \: \: f(2) \\ \\ f(f(2)) = \frac{2f(2) + 1}{3f(2) - 2} \\ \\ f(f(2)) = \frac{ \frac{2 \times 5}{4} + 1}{ \frac{3 \times 5}{4} - 2 } \\ \\ f(f(2)) = \frac{14}{7} \\ \\ f(f(2)) = 2 \\ \\ therefore \: \: \: (fof)(2) = 2 \\ \\ Hence \: \: option \: \: D \: \: is \: \: correct.$