To determine the value of [tex]\( f(5) \)[/tex] for the given function [tex]\( f(x) \)[/tex], we need to carefully consider the conditions specified in the piecewise function definition.
The function [tex]\( f(x) \)[/tex] is defined as follows:
- [tex]\( f(x) = 5 \)[/tex] when [tex]\( x \leq 2 \)[/tex]
- [tex]\( f(x) = 2x - 3 \)[/tex] when [tex]\( x > 2 \)[/tex]
Given [tex]\( x = 5 \)[/tex], we need to determine which condition applies.
1. First, check the condition [tex]\( x \leq 2 \)[/tex]:
- Since [tex]\( 5 \)[/tex] is not less than or equal to [tex]\( 2 \)[/tex], we do not use [tex]\( f(x) = 5 \)[/tex].
2. Next, check the condition [tex]\( x > 2 \)[/tex]:
- Since [tex]\( 5 \)[/tex] is greater than [tex]\( 2 \)[/tex], we will use [tex]\( f(x) = 2x - 3 \)[/tex].
Now, substitute [tex]\( x = 5 \)[/tex] into the equation [tex]\( f(x) = 2x - 3 \)[/tex] to evaluate [tex]\( f(5) \)[/tex]:
[tex]\[
f(5) = 2(5) - 3
\][/tex]
Calculate the value:
[tex]\[
f(5) = 10 - 3 = 7
\][/tex]
Therefore, [tex]\( f(5) \)[/tex] is [tex]\( 7 \)[/tex].
So, the value of [tex]\( f(5) \)[/tex] is [tex]\( 7 \)[/tex].
