true or false, about one to one functions

Question

Decide if the statement is true or false.
If the function

y = g(x)
is strictly decreasing, then

y = |g(x)|
must be a one-to-one function.

 

So I think its true because if its strictly decreasing it must be linear, and if it is linear than it is a one to one function right? I'm not entirely sure because I'm a little confused on the difference between the equations I suppose.

 

Answer 1

False.  If g is strictly decreasing, it may look like a st. line with negative slope, but when its absolute value occurs, the new graphed function has a V-shape, and that one would fail the Horizontal Line test, so it would not be 1-to-1. This counterexample is sufficient to answer the question.

Answer 2

For the function: y = [ g(X) ]

 

you would have several instances where two X values

were going to the same Y value

 

This would fail the one - to - one idea that every Y value

is paired with exactly one X value

 

Therefor it is not a one - to - one function