81 The range of the function \( f(x)=2-x^{2}, x \neq 0 \) is \( \ldots \ldots \ldots \ldots \ldots \) \( \begin{array}{llll}\text { (a) }]-\infty, 2] & \text { (b) }] 2, \infty[ & \text { (c) }] 0,2] & \text { (d) }[0,2]\end{array} \)

To find the range of the function \( f(x) = 2 - x^2 \) where \( x \neq 0 \), we can start by analyzing the function itself. This function represents a downward-opening parabola with a vertex at \( (0, 2) \). The maximum value of the function occurs at \( x = 0 \), yielding \( f(0) = 2 \). As \( x \) moves away from \( 0 \) — either positive or negative — the value of \( f(x) \) decreases without bound. Thus, the function can take any value less than or equal to 2, while it never actually reaches or includes the value for \( x = 0 \). Therefore, the range is \( (-\infty, 2] \). So the answer is: \( \text{(a) } ]-\infty, 2] \)