a) f(x) = -3x+4 how do I determine if this is a bijection or not?
2007-01-21 07:43:44 · 4 answers · asked by Johnny O 1 in Science & Mathematics ➔ Mathematics
If there is one y for every x and one x for every y
domain=(-inf,inf) range=(-inf,inf) and the equation passes both vertical and horizontal line tests.
If the inverse of the function is also a function.
2007-01-21 07:49:15 · answer #1 · answered by Ben B 4 · 0⤊ 0⤋
A bijection is both injective and surjective, so you need to prove both.
Injective: prove this:
(no two points in the domain map to the same point in the range)
If f(x1) = f(x2) then x1=x2
Surjective: prove this:
For every y in R there exists and x in R such that f(x) = y.
( the range of the function 'fills' R)
Any straight line that is not horizontal or vertical is bijective. Draw a little sketch to see that there's only one y value for every x value and for every y value there is a corrosponding x value.
2007-01-21 15:52:36 · answer #2 · answered by modulo_function 7 · 1⤊ 0⤋
If you can invert it, it is a bijection. In this case it is.
Set y = -3x+4 then x=(y-4)/(-3). That's it
2007-01-21 15:49:00 · answer #3 · answered by gianlino 7 · 0⤊ 1⤋
This must be rather new Mathematics. I've never heard of a bijection.
Having now seen the answers below, I see it's not new Mathematics at all -- just some fancy words.
2007-01-21 15:48:11 · answer #4 · answered by Hy 7 · 0⤊ 3⤋