Question

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

A.(f + g)(x) > 3 for all values of x
B.(f + g)(x) < 3 for all values of x
C.(f + g)(x) < 6 for all values of x
D.(f + g)(x) > 6 for all values of x

Answer 1

Explanation:

the value of (f + g)(x) is (f + g)(x) less equal to 3 for all values of x.

Answer 2

For this case we have the following functions:
`f (x) = | x | +9\\g (x) = - 6`

We must find (f + g) (x):

By definition we have to:
`(f + g) (x) = f (x) + g (x)`

So:

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

Thus, for every value of x the function will be positive and greater than or equal to 3.

If
`x = 0`, the function is 3

Answer:

Option A...