Help a soldier in iraq please?

Question

How many solutions are there to | x + 2 | = -14?

a)1

b)2

c)-16

d) None of the above

Over what interval of the domain is this function neither increasing nor decreasing: f(x) = x2 + 4?

a. x = [0]

b. x ∈ (-∞, 0)

c. x ∈ (0, ∞)

d. f(x) ∈ (4, ∞)

Over what interval of the domain is this function decreasing: f(x) = x + 4

a. x ∈ (-∞, 4)

b. x ∈ (-∞, ∞)

c. x ∈ (-4, ∞)

d. Never

Answer 1

First, recall that the function modulus (or "absolute value") yields non-negative numbers. In other words, for all values of y, | y | >=0.

Next note that - 14 < 0 , which implies that there exist *no* y such that

| y | = - 14. This in turn implies that there are *no* solutions to your equation.

The answer is d)

Take the derivative: f ' (x) = 2x. A function is neither increasing nor decreasing whenever its derivative is zero. Thus you are looking for x such that f ' (x) = 0. This yields 2x = 0, or x = [0]

The answer is a)

Again, take the derivative f ' (x) = 1. A function is decreasing whenever its derivative is negative. So you are looking for x such that

f ' (x) < 0, or 1 < 0 which is never true. Thus your function is never decreasing.

The answer is d)