Let's determine the function [tex]\( h(x) \)[/tex] which is the sum of the functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex].
First, we have the functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] given as:
[tex]\[ f(x) = x^2 - 3x + 5 \][/tex]
[tex]\[ g(x) = 2x^2 - 4x - 11 \][/tex]
To find [tex]\( h(x) \)[/tex], we simply add the two functions together:
[tex]\[ h(x) = f(x) + g(x) \][/tex]
Let’s add the expressions term by term:
1. For the [tex]\( x^2 \)[/tex] terms:
[tex]\[ x^2 + 2x^2 = 3x^2 \][/tex]
2. For the [tex]\( x \)[/tex] terms:
[tex]\[ -3x - 4x = -7x \][/tex]
3. For the constant terms:
[tex]\[ 5 - 11 = -6 \][/tex]
Putting these together, we get:
[tex]\[ h(x) = 3x^2 - 7x - 6 \][/tex]
So the correct form of [tex]\( h(x) \)[/tex] is:
[tex]\[ h(x) = 3x^2 - 7x - 6 \][/tex]
Among the given options, this matches with:
[tex]\[ h(x) = 3x^2 - 7x - 6 \][/tex]
Thus, the correct option is:
[tex]\[
\boxed{3x^2 - 7x - 6}
\][/tex]
