To determine the value of [tex]\( f(1) - g(3) \)[/tex], we will follow these steps:
1. Evaluate [tex]\( f(1) \)[/tex]:
- The function [tex]\( f(x) \)[/tex] is given by [tex]\( f(x) = x^2 + 2x + 1 \)[/tex].
- To find [tex]\( f(1) \)[/tex], substitute [tex]\( x = 1 \)[/tex] into the function.
[tex]\[
f(1) = (1)^2 + 2(1) + 1
\][/tex]
[tex]\[
f(1) = 1 + 2 + 1
\][/tex]
[tex]\[
f(1) = 4
\][/tex]
2. Evaluate [tex]\( g(3) \)[/tex]:
- The function [tex]\( g(x) \)[/tex] is given by [tex]\( g(x) = 3x + 5 \)[/tex].
- To find [tex]\( g(3) \)[/tex], substitute [tex]\( x = 3 \)[/tex] into the function.
[tex]\[
g(3) = 3(3) + 5
\][/tex]
[tex]\[
g(3) = 9 + 5
\][/tex]
[tex]\[
g(3) = 14
\][/tex]
3. Calculate [tex]\( f(1) - g(3) \)[/tex]:
- We now have [tex]\( f(1) = 4 \)[/tex] and [tex]\( g(3) = 14 \)[/tex].
- To find [tex]\( f(1) - g(3) \)[/tex], subtract [tex]\( g(3) \)[/tex] from [tex]\( f(1) \)[/tex].
[tex]\[
f(1) - g(3) = 4 - 14
\][/tex]
[tex]\[
f(1) - g(3) = -10
\][/tex]
Thus, the value of [tex]\( f(1) - g(3) \)[/tex] is [tex]\( -10 \)[/tex]. Hence, the correct answer is:
(3) [tex]\(-10 \)[/tex]
