Answer: The correct option is (A) [tex]x^2+2x-6.[/tex]
Step-by-step explanation: We are given the following two functions :
[tex]f(x)=2x+1,\\\\g(x)=x^2-7.[/tex]
We are to find the value of [tex](f+g)(x).[/tex]
We know that
for any two functions p(x) and q(x), we have
[tex](p+q)(x)=p(x)+q(x).[/tex]
Therefore, we get
[tex](f+g)(x)\\\\=f(x)+g(x)\\\\=(2x+1)+(x^2-7)\\\\=2x+1+x^2-7\\\\=x^2+2x-6.[/tex]
Thus, option (A) is CORRECT.
