KCET · Maths · Three Dimensional Geometry
If \( f: R \rightarrow R \) is defined by \( f(x)=\frac{x}{x^{2}+1} \) find \( f(f(2)) \)
- A \( \frac{1}{29} \)
- B \( \frac{10}{29} \)
- C \( \frac{29}{10} \)
- D \( \frac{5}{29} \)
Answer & Solution
Correct Answer
(B) \( \frac{10}{29} \)
Step-by-step Solution
Detailed explanation
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, \( f(f(2))=\frac{\frac{2}{5}}{\left(\frac{2}{5}\right)^{2}+1} \)
\( =\frac{\frac{2}{5}}{\frac{4}{25}+1}=\frac{10}{4+25}=\frac{10}{29} \)
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