Question

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

(f + g(x)>3 for all values of x
(f + g)(x)<3 for all values of x
(f + g)(x)>6 for all values of x
(f + g)(x)<6 for all values of x

Answer 1

Answer: for all values of x

Explanation:

`(f+g)(x)=|x|+9-6=|x|+3`

Since the range of y = |x| is
`y \geq 0`, adding 3 to this shifts the graph 3 units up, giving us that
`(f+g)(x) \geq 3` for all values of x.