Answer :
Sure, let's break down how to find [tex]\( f(2) \)[/tex] step-by-step using the piecewise function:
1. Identify the domain:
- We have several domain categories:
- [tex]\( x \leq -1 \)[/tex]
- [tex]\( -1 < x < 3 \)[/tex]
- [tex]\( x \geq 3 \)[/tex]
2. Determine which domain [tex]\( 2 \)[/tex] fits into:
- We see that [tex]\( 2 \)[/tex] satisfies the condition [tex]\( -1 < 2 < 3 \)[/tex].
- Therefore, [tex]\( 2 \)[/tex] falls into the category [tex]\( -1 < x < 3 \)[/tex].
3. Apply the function corresponding to the domain [tex]\( -1 < x < 3 \)[/tex]:
- The function for this domain is [tex]\( f(x) = 2x + 4 \)[/tex].
4. Calculate [tex]\( f(2) \)[/tex] using the function [tex]\( f(x) = 2x + 4 \)[/tex]:
- Substituting [tex]\( x = 2 \)[/tex] into the function:
[tex]\[ f(2) = 2(2) + 4 \][/tex]
5. Perform the calculation:
- First, we do the multiplication:
[tex]\[ 2(2) = 4 \][/tex]
- Next, we add the 4:
[tex]\[ 4 + 4 = 8 \][/tex]
Therefore, [tex]\( f(2) = 8 \)[/tex].
1. Identify the domain:
- We have several domain categories:
- [tex]\( x \leq -1 \)[/tex]
- [tex]\( -1 < x < 3 \)[/tex]
- [tex]\( x \geq 3 \)[/tex]
2. Determine which domain [tex]\( 2 \)[/tex] fits into:
- We see that [tex]\( 2 \)[/tex] satisfies the condition [tex]\( -1 < 2 < 3 \)[/tex].
- Therefore, [tex]\( 2 \)[/tex] falls into the category [tex]\( -1 < x < 3 \)[/tex].
3. Apply the function corresponding to the domain [tex]\( -1 < x < 3 \)[/tex]:
- The function for this domain is [tex]\( f(x) = 2x + 4 \)[/tex].
4. Calculate [tex]\( f(2) \)[/tex] using the function [tex]\( f(x) = 2x + 4 \)[/tex]:
- Substituting [tex]\( x = 2 \)[/tex] into the function:
[tex]\[ f(2) = 2(2) + 4 \][/tex]
5. Perform the calculation:
- First, we do the multiplication:
[tex]\[ 2(2) = 4 \][/tex]
- Next, we add the 4:
[tex]\[ 4 + 4 = 8 \][/tex]
Therefore, [tex]\( f(2) = 8 \)[/tex].