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

A

Explanation:

Answer 2

The range of values of
`(f + g)(x) \ge 3` is for all values of x
`-\infty` to
`+\infty`

Explanation:

Given

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

`g(x) = -6`

Required

Describe the range of
`(f+g)(x)`

First, calculate
`(f+g)(x)`

`(f+g)(x) = f(x) + g(x)`

Substitute values for f(x) and g(x)

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

Evaluate Like Terms

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

The above expression shows that
`(f + g)(x) \ge 3`

Because
`|x| \ge 0`

Hence, the range of values of
`(f + g)(x) \ge 3` is for all values of x
`-\infty` to
`+\infty`