Question

If $f:R\to R$ is defined by $f\left(x\right)=\frac{x}{x^2+1}$, find $f\left(f\right(2\left)\right)$

• A. $\frac{1}{29}$
• B. $\frac{10}{29}$
• C. $\frac{29}{10}$
• D. $29$

Answer 1

Answer: (B)

$\frac{10}{29}$

We have, $f\left(x\right)=\frac{x}{x^2+1}$

So, $f\left(2\right)=\frac{2}{2^2+1}=\frac{2}{5}$

Hence $f\left(f\right(2\left)\right)=f\left(\frac{2}{5}\right)=\frac{\frac{2}{5}}{{\left(\frac{2}{5}\right)}^2+1}=\frac{2\cdot 5}{5^2+2^2}=\frac{10}{29}$