Calculus
posted by Elisabeth on .
Is x^2  2x
1 to 1?
I keep getting yes every way I try to work it. Book says no. In the end, I get (with x1=1 and x2=1 < I use these numbers because of the x^2) f(x1) = 1 and f(x2)=3. I can't seem to find if x1 = x2
(btw, I know that by the graph it is not, but I am trying to work it out the books way)

I should add that my prof said in the notes that if the two answers to the two functions are the same, then it is not 1 to 1 BECAUSE they have the same answer. That's what has me confused.

Onetoone is usually associated with an interval. If the interval is not mentioned, we will assume that it is (∞∞).
To find out if a function
f(x) is onetoone on the interval, we need to know if it is possible to find different values of x1 and x2 for which f(x1)=f(x2), where x1x2≠0.
If f(x1)=f(x2) then f(x) is not onetoone on the given interval.
For example,
f(x)=x² on the interval (∞,∞),
we can find
f(1)=f(1), or f(2)=f(2), therefore f(x)=x² is NOT onetoone.
The horizontal line test says that if you can draw a horizontal line and intersect the function at two or more points, the function is NOT onetoone. On the other hand, if it is impossible to do so, the function is onetoone.
Try out your problem and post if you have other questions.