Discussion

Explanation:

When x = 2, f(x) = 1/(1 + x)

$f^3\left(2\right)=\frac{1}{1+2}=\frac{1}{3},f^2\left(2\right)=f\left(f\right(2\left)\right)=f\left(\frac{1}{3}\right)=f\left(\frac{1}{3}\right)=\frac{1}{1+{\displaystyle \frac{1}{3}}}=\frac{3}{4}$

$f^3\left(2\right)=f\left(\frac{3}{4}\right)=\frac{1}{1+{\displaystyle \frac{3}{4}}}=\frac{4}{7}$

$f^4\left(2\right)=f\left(\frac{4}{7}\right)=\frac{1}{1+{\displaystyle \frac{4}{7}}}=\frac{7}{11}$

$f^5\left(2\right)=f\left(\frac{7}{11}\right)=\frac{1}{1+{\displaystyle \frac{7}{11}}}=\frac{11}{18}$

∴ f(2)f²(2)f³(2)f⁴(2)f⁵(2)=$\frac{1}{3}\times \frac{3}{4}\times \frac{4}{7}\times \frac{7}{11}\times \frac{11}{18}=\frac{1}{18}$

Hence, option (c).

Hence, option (c).

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