To find [tex]\( f(-2) \)[/tex] for the function [tex]\( f(x) = \frac{3 - x^2}{3 - x} \)[/tex], we follow these steps:
1. Substitute [tex]\( x = -2 \)[/tex] into the function:
[tex]\[
f(-2) = \frac{3 - (-2)^2}{3 - (-2)}
\][/tex]
2. Calculate the numerator:
[tex]\[
3 - (-2)^2 = 3 - 4 = -1
\][/tex]
3. Calculate the denominator:
[tex]\[
3 - (-2) = 3 + 2 = 5
\][/tex]
4. Ensure the denominator is not zero:
Since the denominator [tex]\( 3 + 2 \neq 0 \)[/tex], we can proceed with the division.
5. Divide the numerator by the denominator:
[tex]\[
f(-2) = \frac{-1}{5} = -0.2
\][/tex]
So, the value of [tex]\( f(-2) \)[/tex] is:
[tex]\[
f(-2) = -0.2
\][/tex]
Therefore, [tex]\( f(-2) = -0.2 \)[/tex] and the intermediate calculations were:
- Numerator: [tex]\(-1\)[/tex]
- Denominator: [tex]\(5\)[/tex]
