Functions
If f(x) = (1 - x)/(1 + x), then f(f(x)) equals
Select the correct option:
Solution
x
- Composition: Substitute the entire expression back into itself.
- f(f(x))=1+(1+x1−x)1−(1+x1−x)
- Simplify Numerator and Denominator:
- Numerator: 1+x(1+x)−(1−x)=1+x2x
- Denominator: 1+x(1+x)+(1−x)=1+x2
- Final Ratio: 2/(1+x)2x/(1+x)=x.
- Conclusion: The function is its own inverse (f∘f=I), also known as an involutory function.
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About This Question
- Subject
- mathematics
- Chapter
- sets, relations and functions
- Topic
- functions
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
x
- Composition: Substitute the entire expression back into itself.
- f(f(x))=1+(1+x1−x)1−(1+x1−x)
- Simplify Numerator and Denominator:
- Numerator: 1+x(1+x)−(1−x)=1+x2x
- Denominator: 1+x(1+x)+(1−x)=1+x2
- Final Ratio: 2/(1+x)2x/(1+x)=x.
- Conclusion: The function is its own inverse (f∘f=I), also known as an involutory function.
This medium difficulty mathematics question is from the chapter sets, relations and functions, covering the topic of functions. It appeared in the 2025 exam.
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