To find the limit of [tex]\( f(x) = 9 - x \)[/tex] as [tex]\( x \)[/tex] approaches 4, we need to determine the value that the function approaches as [tex]\( x \)[/tex] gets closer and closer to 4.
Here are the steps to solve for the limit:
1. Understand the function: The function we are given is [tex]\( f(x) = 9 - x \)[/tex]. This is a linear function, and it is continuous everywhere. This means we can directly substitute the value of [tex]\( x \)[/tex] into the function to find the limit.
2. Substitute the approaching value: To find [tex]\(\lim_{{x \to 4}}(9 - x)\)[/tex], we substitute [tex]\( x = 4 \)[/tex] into the function.
3. Perform the substitution:
[tex]\[
f(4) = 9 - 4
\][/tex]
4. Compute the result:
[tex]\[
9 - 4 = 5
\][/tex]
Therefore, the limit of [tex]\( 9 - x \)[/tex] as [tex]\( x \)[/tex] approaches 4 is 5. Thus, we can write:
[tex]\[
\lim_{{x \to 4}} (9 - x) = 5
\][/tex]
This concludes our detailed step-by-step solution for finding the limit.
