If [tex]f(x)=2x^2+1[/tex] and [tex]g(x)=x^2-7[/tex], find [tex](f+g)(x)[/tex].

A. [tex]x^2-6[/tex]
B. [tex]x^2+8[/tex]
C. [tex]3x^2+8[/tex]
D. [tex]3x^2-6[/tex]



Answer :

To determine [tex]\((f + g)(x)\)[/tex], we need to sum the functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex].

Given:
[tex]\[ f(x) = 2x^2 + 1 \][/tex]
[tex]\[ g(x) = x^2 - 7 \][/tex]

First, let's add these two functions together:

[tex]\[ (f + g)(x) = f(x) + g(x) \][/tex]

Substitute the expressions for [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:

[tex]\[ (f + g)(x) = (2x^2 + 1) + (x^2 - 7) \][/tex]

Next, combine like terms:

[tex]\[ (f + g)(x) = 2x^2 + x^2 + 1 - 7 \][/tex]
[tex]\[ (f + g)(x) = 3x^2 - 6 \][/tex]

So, the resulting function is:

[tex]\[ (f + g)(x) = 3x^2 - 6 \][/tex]

Therefore, the correct answer is:

D. [tex]\(3x^2 - 6\)[/tex]