To find the formula for [tex]\((f+g)(x)\)[/tex], we need to add the functions [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] together. Both functions are given as:
[tex]\[ f(x) = x^2 - 10x + 25 \][/tex]
[tex]\[ g(x) = x^2 - 10x + 24 \][/tex]
To determine [tex]\( (f+g)(x) \)[/tex], we add corresponding terms from [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
1. Add the [tex]\( x^2 \)[/tex] terms:
[tex]\[
x^2 + x^2 = 2x^2
\][/tex]
2. Add the [tex]\( -10x \)[/tex] terms:
[tex]\[
-10x + (-10x) = -20x
\][/tex]
3. Add the constant terms:
[tex]\[
25 + 24 = 49
\][/tex]
Putting these results together, we have:
[tex]\[ (f+g)(x) = 2x^2 - 20x + 49 \][/tex]
So, the complete formula for [tex]\( (f+g)(x) \)[/tex] is:
[tex]\[ (f+g)(x) = 2x^2 - 20x + 49 \][/tex]
Therefore,
[tex]\[ (f+g)(x) = 2x^2 - 20x + 49 \][/tex]
