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

Solution:

Given: Functions are f(x) = |x| + 9 and g(x) = -6

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

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

= |x| + 3

(f + g)(x) = x + 3 if x ≥ 0

(f + g)(x) = -x + 3 if x < 0

Therefore, (f + g)(x) ≥ 3 is true for all values of x.

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

Summary:

If f(x) = |x| + 9 and g(x) = -6, then the value of (f + g)(x) ≥ 3 is true for all values of x.