Given:
Consider the below figure attached with this question.
To find:
The value of [tex](f+g)(x)[/tex].
Solution:
The given functions are:
[tex]f(x)=|x|+9[/tex]
[tex]g(x)=-6[/tex]
Now,
[tex](f+g)(x)=f(x)+g(x)[/tex]
[tex](f+g)(x)=|x|+9+(-6)[/tex]
[tex](f+g)(x)=|x|+9-6[/tex]
[tex](f+g)(x)=|x|+3[/tex]
We know that,
[tex]|x|\geq 0[/tex]
Adding 3 on both sides, we get
[tex]|x|+3\geq 0+3[/tex]
[tex](f+g)(x)\geq 3[/tex]
So, [tex](f+g)(x)\geq 3[/tex] for all values of x.
Hence, the correct option is A.
