Does the function f(x) = |x| - 2 have an inverse? If it does, what is the rule for the inverse? If not, why not?

rule-the-inverse

#1

Does the function f(x) = |x| - 2 have an inverse? If it does, what is the rule for the inverse? If not, why not?

Answer:

Swap the x and y then solve for y.
y = |x| - 2
x = |y| - 2 (swap)
x+2 = |y|

This makes the inverse

y=±(x+2) , in other words, y = (x+2) OR -(x+2)

Because there are now two possible y values for each x value (except at the vertex), in general the inverse of absolute value functions are not functions themselves, unless you restrict the domain of the original function to an appropriate portion.