Let A=\{x\in \mathbb{R}:-1 \lt x \lt 1\}. Which of the following is/are bijective functions from A to itself? 1. f(x)=x|x| 2. g(x)=\cos(\pi x) Select the correct answer using the code given below:
- A. 1 only ✓
- B. 2 only
- C. Both 1 and 2
- D. Neither 1 nor 2
Correct Answer: A. 1 only
Explanation
f(x) = x|x| is strictly increasing (x^2 for x \geq 0, -x^2 for x \lt 0) and maps (-1, 1) to (-1, 1), making it bijective. g(x) = \cos(\pi x) maps (-1, 1) to (-1, 1]. Since g(x) = g(-x), it is not one-to-one.
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