Search any question & find its solution
Question:
Answered & Verified by Expert
If \( f: R \rightarrow R \) is defined by \( f(x)=\frac{x}{x^{2}+1} \) find \( f(f(2)) \)
Options:
Solution:
2906 Upvotes
Verified Answer
The correct answer is:
\( \frac{10}{29} \)
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, \( f(f(2))=\frac{\frac{2}{5}}{\left(\frac{2}{5}\right)^{2}+1} \)
\( =\frac{\frac{2}{5}}{\frac{4}{25}+1}=\frac{10}{4+25}=\frac{10}{29} \)
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.