Functions
The function f(x) = |x| - x is
Select the correct option:
Solution
Neither even nor odd
- Even Property Check: Requires f(βx)=f(x).
- f(βx)=β£βxβ£β(βx)=β£xβ£+x.
- This is not equal to β£xβ£βx for all xξ =0. Not even.
- Odd Property Check: Requires f(βx)=βf(x).
- βf(x)=β(β£xβ£βx)=xββ£xβ£.
- This is not equal to β£xβ£+x for all x. Not odd.
- Logical Verification: For x=1,f(1)=0. For x=β1,f(β1)=2. Since f(β1) is neither f(1) nor βf(1), the function is neither even nor odd.
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About This Question
- Subject
- mathematics
- Chapter
- sets, relations and functions
- Topic
- functions
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
Neither even nor odd
- Even Property Check: Requires f(βx)=f(x).
- f(βx)=β£βxβ£β(βx)=β£xβ£+x.
- This is not equal to β£xβ£βx for all xξ =0. Not even.
- Odd Property Check: Requires f(βx)=βf(x).
- βf(x)=β(β£xβ£βx)=xββ£xβ£.
- This is not equal to β£xβ£+x for all x. Not odd.
- Logical Verification: For x=1,f(1)=0. For x=β1,f(β1)=2. Since f(β1) is neither f(1) nor βf(1), the function is neither even nor odd.
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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