5. Find the domain for the function \( f(x)=\frac{1-x^{2}}{x^{2}-4} \) \( \begin{array}{lll}\text { a) } R \backslash\{-2,2\} & \text { b) } R \backslash[-2,2] & \text { c) }[-2,2] \\ \text { d) }(-2,2) & \text { e) None of these }\end{array} \)

To find the domain of the function \( f(x)=\frac{1-x^{2}}{x^{2}-4} \), we need to identify the values of \( x \) that would make the denominator zero, as these values cannot be included in the domain. The denominator \( x^{2}-4 \) can be factored as \( (x-2)(x+2) \), which gives us the critical points \( x = -2 \) and \( x = 2 \). Therefore, the function is undefined at these points. Thus, the domain of the function is all real numbers except \( -2 \) and \( 2 \), which can be written as \( R \backslash \{-2, 2\} \). Therefore, the answer is option **a)** \( R \backslash \{-2, 2\} \). The final answer is **a)** \( R \backslash \{-2, 2\} \).