Find the formula for [tex](f+g)(x)[/tex].

Given:
[tex]f(x)=x^2 - 10x + 25[/tex]
[tex]g(x)=x^2 - 10x + 24[/tex]

[tex](f+g)(x) = 2x^2 - 20x + 49[/tex]



Answer :

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]