To determine the value of [tex]\( p(-1) \)[/tex] for the function [tex]\( p(x) = \frac{1}{x - 2} \)[/tex], we need to follow these steps carefully:
1. Identify the function: We are given the function [tex]\( p(x) = \frac{1}{x - 2} \)[/tex].
2. Substitute the given value into the function: We are asked to find [tex]\( p(-1) \)[/tex]. Thus, we will substitute [tex]\( x = -1 \)[/tex] into the function.
3. Perform the substitution:
[tex]\[
p(-1) = \frac{1}{-1 - 2}
\][/tex]
4. Simplify the expression in the denominator:
[tex]\[
-1 - 2 = -3
\][/tex]
5. Complete the calculation:
[tex]\[
p(-1) = \frac{1}{-3} = -\frac{1}{3}
\][/tex]
Therefore, the value of [tex]\( p(-1) \)[/tex] is [tex]\( -\frac{1}{3} \)[/tex].
So, the correct answer is:
[tex]\[ -\frac{1}{3} \][/tex]
