Let `A}x :-1lt=xlt=1}a n df: Avec` such that `f(x)=x|x|,` then `f` is a bijection (b) injective but not surjective Surjective but not injective (d) neither injective nor surjective

Explanation

To determine the nature of the function \( f(x) = x |x| \) defined on the interval \( A = \{ x \mid -1 < x < 1 \} \), we need to analyze its injectivity and surjectivity.

### Step 1: Understand the function
The function \( f(x) = x |x| \) can be rewritten based on the sign of \( x \):
- For \( x < 0 \): \( f(x) = x(-x) = -x^2 \)
- For \( x \geq 0 \): \( f(x) = x(x) = x^2 \)

### Step 2: Analyze the function on the interval
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