Question

If f(x) = (x + 9 and g(x) = --6, which describes the range of (f + g)(x)?

Answer 1

Given:

Consider the below figure attached with this question.

To find:

The value of $(f+g)(x)$.

Solution:

The given functions are:

$f(x)=|x|+9$

$g(x)=-6$

Now,

$(f+g)(x)=f(x)+g(x)$

$(f+g)(x)=|x|+9+(-6)$

$(f+g)(x)=|x|+9-6$

$(f+g)(x)=|x|+3$

We know that,

$|x|\geq 0$

Adding 3 on both sides, we get

$|x|+3\geq 0+3$

$(f+g)(x)\geq 3$

So, $(f+g)(x)\geq 3$ for all values of x.

Hence, the correct option is A.