Question

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

A. (f + g)(x) more than equal to 3 for all values of x
B. (f + g)(x) less than equal to 3 for all values of x
C. (f + g)(x) less than equal to 6 for all values of x
D. (f + g)(x) more than equal to 6 for all values of x

Answer 1

The value of (f + g)(x) is |x| + 3. It is more than equal to 3 for all values of x.

Step-by-step explanation:

The question asks about the sum of two functions, f(x) and g(x). We have f(x) = |x| + 9 and g(x) = -6. To find the sum, we simply add the values of f(x) and g(x) for the given input x. So, (f + g)(x) = |x| + 9 - 6 = |x| + 3.

Since the absolute value function always gives a non-negative value, we have (f + g)(x) ≥ 3 for all values of x. Therefore, the correct option is A. (f + g)(x) more than equal to 3 for all values of x.