Question

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

(f + g)(x)≥3 for all values of x

Explanation:

Given the expressions f(x) = |x| + 9 and g(x) = –6, sine f(x) contains the absolute value of a variable x, this absolute value can be negative and positive. Therefore f(x) can be expressed in two forms as shown;

f(x) = x+9 and f(x) = -x+9

If f(x) = x+ 9 and g(x) = -6

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

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

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

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

Similarly, if f(x) = -x+ 9 and g(x) = -6

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

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

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

(f + g)(x) = -x+3

(f + g)(x) = 3-x

In both expresson, we have bith x to be positive and negative, hence we can write the value of resulting x as an absolute value as shown;

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

This shows that (f + g)(x)≥3 for all values of x