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

Question

Camille Burgess

Mathematics

2 February, 01:36

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

+2

Answers (1)

Know the Answer?

Willie Hunt · Answer 1

Answer (a)

Step-by-step explanation:

(f + g) (x) would be equal to |x| + 9 - 6, which reduces to |x| + 3.

Since |x| cannot be less than zero, the range of this composite function

(f + g) (x) = |x| + 3 is [3, infinity). That is, the smallest value is 3. This corresponds to Answer (a).