Q83 / 180 · KCET 2015 · Mathematics
If \( f: R \rightarrow R \) is defined by \( f(x)=\frac{x}{x^{2}+1} \) find \( f(f(2)) \)
- A\( \frac{1}{29} \)
- Correct answerB\( \frac{10}{29} \)
- C\( \frac{29}{10} \)
- D\( \frac{5}{29} \)
Solution
Given that, \( f(x)=\frac{x}{x^{2}+1} \rightarrow(1) \)
At \( x=2 \), we have \( f(2)=\frac{2}{2^{2}+1}=\frac{2}{5} \)
So, \( f(f(2))=\frac{\frac{2}{5}}{\left(\frac{2}{5}\right)^{2}+1} \)
\( =\frac{\frac{2}{5}}{\frac{4}{25}+1}=\frac{10}{4+25}=\frac{10}{29} \)
At \( x=2 \), we have \( f(2)=\frac{2}{2^{2}+1}=\frac{2}{5} \)
So, \( f(f(2))=\frac{\frac{2}{5}}{\left(\frac{2}{5}\right)^{2}+1} \)
\( =\frac{\frac{2}{5}}{\frac{4}{25}+1}=\frac{10}{4+25}=\frac{10}{29} \)
Hence, the correct answer is option: 'B'.