: I have come to a point in solving : is this function one-to-one, where the absolute value of a = the absolute value of b. Can this be one to one?
For the record, the problem states: f(x)= |x| - 2
I assigned a and b, and equal them to each other.
|a| - 2 = |b| - 2 ; add two to both sides
|a| = |b|
therefore a = b? or not really?
No it does not! for instance we could take a=3 and b=-3, then
|3| = |-3|
Another way to say it is it's not one-to-one because,
for instance f(3) = f(-3) = 1 but 3 does not equal -3.
The points (3,1) and (-3,1) are both on the graph and
a horizontal line goes through them both, so the graph does not pass the horizontal line test.
The graph looks like this:
And as you see, the horizontal lines cut it more than
once, so it cannot be one-to-one.
Edwin