Question

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

Answer 1

a) (f + g)(x) ≥ 3 for all values of x.

Explanation:

Given:

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

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

Now plug in the given functions

= l x l + 9 + (-6) +(-6) = -6

Therefore, (f + g)(x) = l x l + 9 - 6

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

Here the absolute value is always greater than or equal to zero.

So for values of x, lxl ≥ 0

There is already +3,

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

Hope you will understand the concept.

Thank you.