One-to-one — Algebra II, what it means and where it is taught
No two inputs share an output. Only a one-to-one function has an inverse that is itself a function.
Taught in Algebra II.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Function — A rule pairing each input with exactly one output.
What uses it later
This idea is needed for:
- Horizontal line test — If any horizontal line meets a graph twice, the function is not one-to-one.
- Restricted domain — The stretch of the original function kept so that it is one-to-one.
Practise this idea
1 question in the course bank use One-to-one, in Composing & Inverting Functions.
Problem 1
Which function has an inverse that is also a function?
- f(x)=x2
- f(x)=|x|
- f(x)=x3
- f(x)=x2+1
Worked answer
f(x)=x3
x2 and |x| both send two inputs to one output
x3 is one-to-one — it never repeats a value
So only x3 can be undone