Question

Let f be the function given by f(x) = |x| - 2. What is the solution to the equation f(x) = 0?

a) -2
b) 0
c) 2
d) 4

Answer 1

The solution to the equation f(x) = 0 for the function f(x) = |x| - 2 is x = -2, 2.

Step-by-step explanation:

To find the solution to the equation f(x) = 0 for the function f(x) = |x| - 2, we set f(x) equal to zero and solve for x. Here's the step-by-step process:

Set f(x) = 0.

Replace f(x) with the given function.

|x| - 2 = 0

Add 2 to both sides to isolate the absolute value term.

|x| = 2

Since the absolute value of a number is either positive or zero, we can solve this equation by considering two cases:

If x is positive, then x = 2.

If x is negative, then -x = 2. Solving for x gives x = -2.

Therefore, the solution to the equation f(x) = 0 is x = -2, 2.